From eee4a3fe0085b86c1d977e970aa5b1056866ecfc Mon Sep 17 00:00:00 2001 From: Christine Nicole James Date: Thu, 5 Feb 2015 11:43:37 -0500 Subject: [PATCH 01/10] Ising code-first copy --- isingCode.f95 | 161 ++++++++++++++++++++++++++++++++++++++++++++++++++ 1 file changed, 161 insertions(+) create mode 100755 isingCode.f95 diff --git a/isingCode.f95 b/isingCode.f95 new file mode 100755 index 0000000..e8fdf4b --- /dev/null +++ b/isingCode.f95 @@ -0,0 +1,161 @@ +program isingtest + +IMPLICIT NONE + +integer :: i, iteration, delta_energy, N, T +integer :: j, state, energy_new, energy_old +integer :: i_swap_value, j_swap_value +integer :: wholeRand, k +integer, dimension(10,10, 50) :: a +integer, parameter :: out_unit=20 +real, dimension(10,2) :: m + +real :: rand, beta, g, kB + +open (unit=out_unit,file="results.txt",action="write",status="replace") + +! Define Boltzmann Constant + +kB=1.3806488*(10**(-23)) + +! Total number of spots in square lattice + +N=10*10 + + +! The first random value is always the same, so it is +! created and not used + +rand = get_random_number() +wholeRand = get_random_whole_number(rand) + +! Loop through different temperatures +k=1 +do T= 100,1000,100 + + ! Define beta value for new temp + + beta = 1/(kB*T) + + ! Reset all spins in array a to positive 1 + + do state = 1,50 + do i=1,10 + do j=1,10 + a(i,j, state)=1 + end do + end do + end do + + + ! Loop to minimize 50 states + do state = 1,50 + + ! Iterate through random flips 100,000 times to find a minimized energy state + do iteration=1,100000 + + ! Picking random i and j coors to determine which spin to flip + + rand = get_random_number() + i_swap_value = get_random_whole_number(rand) + + rand = get_random_number() + j_swap_value = get_random_whole_number(rand) + + a(i_swap_value, j_swap_value, state) = a(i_swap_value, j_swap_value,state)*(-1) + + rand = get_random_number() + + if (i_swap_value>1) then + energy_new =energy_new+(a(i_swap_value, j_swap_value,state)* a((i_swap_value-1), j_swap_value, state)) + energy_old = energy_old+ (a(i_swap_value, j_swap_value,state)* a((i_swap_value-1), j_swap_value,state)*(-1)) + end if + if (i_swap_value<10) then + energy_new = energy_new+ (a(i_swap_value, j_swap_value,state)* a((i_swap_value+1), j_swap_value, state)) + energy_old = energy_old+ (a(i_swap_value, j_swap_value,state)* a((i_swap_value+1), j_swap_value,state)*(-1)) + end if + if (j_swap_value>1) then + energy_new = energy_new+(a(i_swap_value, j_swap_value,state)* a(i_swap_value, (j_swap_value-1),state)) + energy_old = energy_old+ (a(i_swap_value, j_swap_value,state)* a(i_swap_value, (j_swap_value-1),state)*(-1)) + end if + if (j_swap_value<10) then + energy_new = energy_new+ (a(i_swap_value, j_swap_value,state)* a(i_swap_value, (j_swap_value+1),state)) + energy_old = energy_old+ (a(i_swap_value, j_swap_value,state)* a(i_swap_value, (j_swap_value+1),state)*(-1)) + end if + + ! Multiplying the sum by -J + energy_new = -1*energy_new + energy_old = -1*energy_old + + ! Calculate the change in energy + delta_energy = energy_new- energy_old + + if (delta_energy>0) then + rand = get_random_number() + g = exp((-beta*delta_energy)) + if (g<=rand) then + a(i_swap_value, j_swap_value,state)= a(i_swap_value, j_swap_value,state)*(-1) + end if + end if + + ! Resetting energy values + energy_new=0 + energy_old=0 + end do + + end do + + !Record m for given T value + + m(k,1) = T + m(k,2) = 0 + + do i=1,10 + do j=1,10 + m(k,2)=m(k,2)+a(i,j,state) + end do + end do + + m(k,2)=m(k,2)/N + + write (out_unit,*) m(k,1), m(k,2) + + k=k+1 +end do + +close(out_unit) + + + +contains + + function get_random_number() + integer :: i_seed + integer, dimension(:), ALLOCATABLE :: Set_seed + integer, dimension(1:8) :: dateSet_seed + real :: get_random_number, r + + CALL RANDOM_SEED(size=i_seed) + ALLOCATE(Set_seed(1:i_seed)) + CALL RANDOM_SEED(get=Set_seed) + CALL DATE_AND_TIME(values=dateSet_seed) + Set_seed(i_seed)=dateSet_seed(8) + !Set_seed(2)=dateSet_seed(8) + Set_seed(1)=dateSet_seed(8)*dateSet_seed(6) + CALL RANDOM_SEED(put=Set_seed) + DEALLOCATE(Set_seed) + + CALL RANDOM_NUMBER(r) + get_random_number = r + end function get_random_number + + function get_random_whole_number(y) + integer :: get_random_whole_number + real :: y + get_random_whole_number = (10*y)+1 + if (get_random_whole_number==11) then + get_random_whole_number = (10*y)+1 + end if + end function + +end program isingtest From b676849a987e95d8e44ed485f5dccc5e935fe5dd Mon Sep 17 00:00:00 2001 From: Christine Nicole James Date: Wed, 18 Feb 2015 13:41:28 -0500 Subject: [PATCH 02/10] Bash script which compiles and runs the isingCode.f95 file and plots using the .p files --- isingRunandPlotBashScript.txt | 9 +++++++++ 1 file changed, 9 insertions(+) create mode 100755 isingRunandPlotBashScript.txt diff --git a/isingRunandPlotBashScript.txt b/isingRunandPlotBashScript.txt new file mode 100755 index 0000000..7fcf5f3 --- /dev/null +++ b/isingRunandPlotBashScript.txt @@ -0,0 +1,9 @@ +#!/bin/bash -login + +gfortran isingCode.f95 -o test + +./test + +gnuplot> load create_mvsSteps_Plot.p + +gnuplot> load create_mvsT_Plot.p From 2ed0da5b80e4b66ce84c97ab2b8e66c3bd9dfb07 Mon Sep 17 00:00:00 2001 From: Christine Nicole James Date: Wed, 18 Feb 2015 13:45:52 -0500 Subject: [PATCH 03/10] Latest draft of isingCode, includes the calculations and file writing. --- isingCode.f95 | 577 +++++++++++++++++++++++++++++++++++++++----------- 1 file changed, 453 insertions(+), 124 deletions(-) diff --git a/isingCode.f95 b/isingCode.f95 index e8fdf4b..bcc5c15 100755 --- a/isingCode.f95 +++ b/isingCode.f95 @@ -2,129 +2,444 @@ program isingtest IMPLICIT NONE -integer :: i, iteration, delta_energy, N, T -integer :: j, state, energy_new, energy_old -integer :: i_swap_value, j_swap_value -integer :: wholeRand, k -integer, dimension(10,10, 50) :: a -integer, parameter :: out_unit=20 -real, dimension(10,2) :: m - -real :: rand, beta, g, kB - -open (unit=out_unit,file="results.txt",action="write",status="replace") - -! Define Boltzmann Constant - -kB=1.3806488*(10**(-23)) - -! Total number of spots in square lattice - -N=10*10 - - -! The first random value is always the same, so it is -! created and not used - -rand = get_random_number() -wholeRand = get_random_whole_number(rand) - -! Loop through different temperatures -k=1 -do T= 100,1000,100 - - ! Define beta value for new temp - - beta = 1/(kB*T) - - ! Reset all spins in array a to positive 1 +integer :: i, j, flipSpins, k, Tstep, everyHundred +integer :: size, i_swap_value, j_swap_value +integer :: avgCount, mCount +integer, parameter :: out_unit=20 +integer, parameter :: out_unit2=10 +integer, dimension(100,100) :: spins + +real, dimension(3,7000000) :: m_T +real, dimension(20) :: m_bins +real :: e_new, e_old, delta_e +real :: m, rand, kB, beta, g, T +real :: avgM, m_avg, stdev, diff +real :: diffSq, diffSqSum + +character(len=10) :: out_file +character(len=7) :: out_file_base +character(len=3) :: out_file_no + +size=100 + +kB=1 + +out_file_base="Results" + +open (unit=out_unit2,file="avg_m_values",action="write",status="replace") + +do Tstep=1,2 + + k=1 + + T=Tstep + beta=1/(kB*T) + write(out_file_no,"(F3.1)") T + out_file=out_file_base//out_file_no + open (unit=out_unit,file=out_file,action="write",status="replace") + do i=1,size + do j=1,size + spins(i,j)=1 + end do + end do + + m_Avg=0 + everyHundred=1 + avgCount=1 + mCount=1 + avgM=0 + diffSqSum=0 + do flipSpins=1,5000000 + + rand = get_random_number() + + rand = get_random_number() + i_swap_value = get_random_whole_number(rand,size) + + rand = get_random_number() + j_swap_value = get_random_whole_number(rand,size) + + spins(i_swap_value, j_swap_value)=spins(i_swap_value, j_swap_value)*(-1) + + e_new=0 + e_old=0 + + if (i_swap_value>1) then + e_new=e_new+(spins(i_swap_value,j_swap_value)*spins((i_swap_value-1),j_swap_value)) + e_old=e_old+(spins(i_swap_value,j_swap_value)*spins((i_swap_value-1),j_swap_value)*(-1)) + else + e_new=e_new+(spins(i_swap_value,j_swap_value)*spins((size),j_swap_value)) + e_old=e_old+(spins(i_swap_value,j_swap_value)*spins((size),j_swap_value)*(-1)) + end if + if (j_swap_value>1) then + e_new=e_new+(spins(i_swap_value,j_swap_value)*spins(i_swap_value,(j_swap_value-1))) + e_old=e_old+(spins(i_swap_value,j_swap_value)*spins(i_swap_value,(j_swap_value-1))*(-1)) + else + e_new=e_new+(spins(i_swap_value,j_swap_value)*spins(i_swap_value,(size))) + e_old=e_old+(spins(i_swap_value,j_swap_value)*spins(i_swap_value,(size))*(-1)) + end if + if (i_swap_value0) then + rand=get_random_number() + g=exp((-beta*delta_e)) + if(g<=rand) then + spins(i_swap_value,j_swap_value)=spins(i_swap_value,j_swap_value)*(-1) + end if + end if + + if (everyHundred == 100) then + m=0 + do i=1,size + do j=1,size + m=m+spins(i,j) + end do + end do + + m=m/(size*size) + if (m<0) then + m=(-1)*m + end if + m_T(2,k)=m + m_T(1,k)=flipSpins + m_T(1,k)=m_T(1,k)/1000000.0 + write (out_unit,*) m_T(1,k),m_T(2,k) + + if (flipSpins>2999999) then + m_avg=m_avg+m + if (avgCount==1000) then + m_avg=m_avg/avgCount + avgCount=0 + m_bins(mCount)=m_avg + mCount=mCount+1 + end if + avgCount=avgCount+1 + end if + + end if + + k=k+1 + if (everyHundred==100) then + everyHundred=1 + else + everyHundred=everyHundred+1 + end if + + !Iterations end + end do + mCount=mCount-1 + do i=1,mCount + avgM=avgM+m_bins(i) + end do + avgM=avgM/mCount + + do i=1,mCount + diff=avgM-m_bins(i) + diffSq=diff**2 + diffSqSum=diffSqSum+diffSq + end do + stdev=sqrt((diffSqSum/mCount)) + + write (out_unit2,*) T, avgM, stdev + close(out_unit) + +!Temp end +end do - do state = 1,50 - do i=1,10 - do j=1,10 - a(i,j, state)=1 +do Tstep=1,9 + + k=1 + + T=2+(Tstep/10.0) + beta=1/(kB*T) + write(out_file_no,"(F3.1)") T + out_file=out_file_base//out_file_no + open (unit=out_unit,file=out_file,action="write",status="replace") + do i=1,size + do j=1,size + spins(i,j)=1 + end do + end do + + m_Avg=0 + everyHundred=1 + avgCount=1 + mCount=1 + avgM=0 + diffSqSum=0 + do flipSpins=1,5000000 + + rand = get_random_number() + + rand = get_random_number() + i_swap_value = get_random_whole_number(rand,size) + + rand = get_random_number() + j_swap_value = get_random_whole_number(rand,size) + + spins(i_swap_value, j_swap_value)=spins(i_swap_value, j_swap_value)*(-1) + + e_new=0 + e_old=0 + + if (i_swap_value>1) then + e_new=e_new+(spins(i_swap_value,j_swap_value)*spins((i_swap_value-1),j_swap_value)) + e_old=e_old+(spins(i_swap_value,j_swap_value)*spins((i_swap_value-1),j_swap_value)*(-1)) + else + e_new=e_new+(spins(i_swap_value,j_swap_value)*spins((size),j_swap_value)) + e_old=e_old+(spins(i_swap_value,j_swap_value)*spins((size),j_swap_value)*(-1)) + end if + if (j_swap_value>1) then + e_new=e_new+(spins(i_swap_value,j_swap_value)*spins(i_swap_value,(j_swap_value-1))) + e_old=e_old+(spins(i_swap_value,j_swap_value)*spins(i_swap_value,(j_swap_value-1))*(-1)) + else + e_new=e_new+(spins(i_swap_value,j_swap_value)*spins(i_swap_value,(size))) + e_old=e_old+(spins(i_swap_value,j_swap_value)*spins(i_swap_value,(size))*(-1)) + end if + if (i_swap_value0) then + rand=get_random_number() + g=exp((-beta*delta_e)) + if(g<=rand) then + spins(i_swap_value,j_swap_value)=spins(i_swap_value,j_swap_value)*(-1) + end if + end if + + if (everyHundred == 100) then + m=0 + do i=1,size + do j=1,size + m=m+spins(i,j) end do - end do - end do - - - ! Loop to minimize 50 states - do state = 1,50 - - ! Iterate through random flips 100,000 times to find a minimized energy state - do iteration=1,100000 - - ! Picking random i and j coors to determine which spin to flip - - rand = get_random_number() - i_swap_value = get_random_whole_number(rand) - - rand = get_random_number() - j_swap_value = get_random_whole_number(rand) - - a(i_swap_value, j_swap_value, state) = a(i_swap_value, j_swap_value,state)*(-1) - - rand = get_random_number() - - if (i_swap_value>1) then - energy_new =energy_new+(a(i_swap_value, j_swap_value,state)* a((i_swap_value-1), j_swap_value, state)) - energy_old = energy_old+ (a(i_swap_value, j_swap_value,state)* a((i_swap_value-1), j_swap_value,state)*(-1)) - end if - if (i_swap_value<10) then - energy_new = energy_new+ (a(i_swap_value, j_swap_value,state)* a((i_swap_value+1), j_swap_value, state)) - energy_old = energy_old+ (a(i_swap_value, j_swap_value,state)* a((i_swap_value+1), j_swap_value,state)*(-1)) - end if - if (j_swap_value>1) then - energy_new = energy_new+(a(i_swap_value, j_swap_value,state)* a(i_swap_value, (j_swap_value-1),state)) - energy_old = energy_old+ (a(i_swap_value, j_swap_value,state)* a(i_swap_value, (j_swap_value-1),state)*(-1)) - end if - if (j_swap_value<10) then - energy_new = energy_new+ (a(i_swap_value, j_swap_value,state)* a(i_swap_value, (j_swap_value+1),state)) - energy_old = energy_old+ (a(i_swap_value, j_swap_value,state)* a(i_swap_value, (j_swap_value+1),state)*(-1)) - end if - - ! Multiplying the sum by -J - energy_new = -1*energy_new - energy_old = -1*energy_old - - ! Calculate the change in energy - delta_energy = energy_new- energy_old - - if (delta_energy>0) then - rand = get_random_number() - g = exp((-beta*delta_energy)) - if (g<=rand) then - a(i_swap_value, j_swap_value,state)= a(i_swap_value, j_swap_value,state)*(-1) - end if - end if - - ! Resetting energy values - energy_new=0 - energy_old=0 - end do - - end do - - !Record m for given T value - - m(k,1) = T - m(k,2) = 0 - - do i=1,10 - do j=1,10 - m(k,2)=m(k,2)+a(i,j,state) - end do - end do - - m(k,2)=m(k,2)/N - - write (out_unit,*) m(k,1), m(k,2) - - k=k+1 + end do + + m=m/(size*size) + if (m<0) then + m=(-1)*m + end if + m_T(2,k)=m + m_T(1,k)=flipSpins + m_T(1,k)= m_T(1,k)/1000000 + write (out_unit,*) m_T(1,k),m_T(2,k) + + if (flipSpins>2999999) then + m_avg=m_avg+m + if (avgCount==1000) then + m_avg=m_avg/avgCount + avgCount=0 + m_bins(mCount)=m_avg + mCount=mCount+1 + end if + avgCount=avgCount+1 + end if + + end if + + k=k+1 + if (everyHundred==100) then + everyHundred=1 + else + everyHundred=everyHundred+1 + end if + + !Iterations end + end do + mCount=mCount-1 + do i=1,mCount + avgM=avgM+m_bins(i) + end do + avgM=avgM/mCount + + do i=1,mCount + diff=avgM-m_bins(i) + diffSq=diff**2 + diffSqSum=diffSqSum+diffSq + end do + stdev=sqrt((diffSqSum/mCount)) + + write (out_unit2,*) T, avgM, stdev + close(out_unit) + +!Temp end end do -close(out_unit) +do Tstep=3,4 + + k=1 + + T=Tstep + beta=1/(kB*T) + write(out_file_no,"(F3.1)") T + out_file=out_file_base//out_file_no + open (unit=out_unit,file=out_file,action="write",status="replace") + do i=1,size + do j=1,size + spins(i,j)=1 + end do + end do + + m_Avg=0 + everyHundred=1 + avgCount=1 + mCount=1 + avgM=0 + diffSqSum=0 + do flipSpins=1,5000000 + + rand = get_random_number() + + rand = get_random_number() + i_swap_value = get_random_whole_number(rand,size) + + rand = get_random_number() + j_swap_value = get_random_whole_number(rand,size) + + spins(i_swap_value, j_swap_value)=spins(i_swap_value, j_swap_value)*(-1) + + e_new=0 + e_old=0 + + if (i_swap_value>1) then + e_new=e_new+(spins(i_swap_value,j_swap_value)*spins((i_swap_value-1),j_swap_value)) + e_old=e_old+(spins(i_swap_value,j_swap_value)*spins((i_swap_value-1),j_swap_value)*(-1)) + else + e_new=e_new+(spins(i_swap_value,j_swap_value)*spins((size),j_swap_value)) + e_old=e_old+(spins(i_swap_value,j_swap_value)*spins((size),j_swap_value)*(-1)) + end if + if (j_swap_value>1) then + e_new=e_new+(spins(i_swap_value,j_swap_value)*spins(i_swap_value,(j_swap_value-1))) + e_old=e_old+(spins(i_swap_value,j_swap_value)*spins(i_swap_value,(j_swap_value-1))*(-1)) + else + e_new=e_new+(spins(i_swap_value,j_swap_value)*spins(i_swap_value,(size))) + e_old=e_old+(spins(i_swap_value,j_swap_value)*spins(i_swap_value,(size))*(-1)) + end if + if (i_swap_value0) then + rand=get_random_number() + g=exp((-beta*delta_e)) + if(g<=rand) then + spins(i_swap_value,j_swap_value)=spins(i_swap_value,j_swap_value)*(-1) + end if + end if + + if (everyHundred == 100) then + m=0 + do i=1,size + do j=1,size + m=m+spins(i,j) + end do + end do + + m=m/(size*size) + if (m<0) then + m=(-1)*m + end if + m_T(2,k)=m + m_T(1,k)=flipSpins + m_T(1,k)= m_T(1,k)/1000000 + write (out_unit,*) m_T(1,k),m_T(2,k) + + if (flipSpins>2999999) then + m_avg=m_avg+m + if (avgCount==1000) then + m_avg=m_avg/avgCount + avgCount=0 + m_bins(mCount)=m_avg + mCount=mCount+1 + end if + avgCount=avgCount+1 + end if + + end if + + k=k+1 + if (everyHundred==100) then + everyHundred=1 + else + everyHundred=everyHundred+1 + end if + + !Iterations end + end do + mCount=mCount-1 + do i=1,mCount + avgM=avgM+m_bins(i) + end do + avgM=avgM/mCount + + do i=1,mCount + diff=avgM-m_bins(i) + diffSq=diff**2 + diffSqSum=diffSqSum+diffSq + end do + stdev=sqrt((diffSqSum/mCount)) + + write (out_unit2,*) T, avgM, stdev + close(out_unit) + +!Temp end +end do +close(out_unit2) contains @@ -147,15 +462,29 @@ function get_random_number() CALL RANDOM_NUMBER(r) get_random_number = r - end function get_random_number + end function get_random_number - function get_random_whole_number(y) - integer :: get_random_whole_number + function get_random_whole_number(y,x) + integer :: get_random_whole_number, x real :: y - get_random_whole_number = (10*y)+1 - if (get_random_whole_number==11) then - get_random_whole_number = (10*y)+1 + get_random_whole_number = (x*y)+1 + if (get_random_whole_number==(x+1)) then + get_random_whole_number = (x*y)+1 end if end function + end program isingtest + + +!write (out_unit,*) spins(1,1),spins(1,2),spins(1,3),spins(1,4),spins(1,5),spins(1,6),spins(1,7),spins(1,8),spins(1,9),spins(1,10) +!write (out_unit,*) spins(2,1),spins(2,2),spins(2,3),spins(2,4),spins(2,5),spins(2,6),spins(2,7),spins(2,8),spins(2,9),spins(2,10) +!write (out_unit,*) spins(3,1),spins(3,2),spins(3,3),spins(3,4),spins(3,5),spins(3,6),spins(3,7),spins(3,8),spins(3,9),spins(3,10) +!write (out_unit,*) spins(4,1),spins(4,2),spins(4,3),spins(4,4),spins(4,5),spins(4,6),spins(4,7),spins(4,8),spins(4,9),spins(4,10) +!write (out_unit,*) spins(5,1),spins(5,2),spins(5,3),spins(5,4),spins(5,5),spins(5,6),spins(5,7),spins(5,8),spins(5,9),spins(5,10) +!write (out_unit,*) spins(6,1),spins(6,2),spins(6,3),spins(6,4),spins(6,5),spins(6,6),spins(6,7),spins(6,8),spins(6,9),spins(6,10) +!write (out_unit,*) spins(7,1),spins(7,2),spins(7,3),spins(7,4),spins(7,5),spins(7,6),spins(7,7),spins(7,8),spins(7,9),spins(7,10) +!write (out_unit,*) spins(8,1),spins(8,2),spins(8,3),spins(8,4),spins(8,5),spins(8,6),spins(8,7),spins(8,8),spins(8,9),spins(8,10) +!write (out_unit,*) spins(9,1),spins(9,2),spins(9,3),spins(9,4),spins(9,5),spins(9,6),spins(9,7),spins(9,8),spins(9,9),spins(9,10) +!write(out_unit,*)spins(10,1),spins(10,2),spins(10,3),spins(10,4),spins(10,5),spins(10,6),spins(10,7),spins(10,8),spins(10,9) +!write (out_unit,*) ' ' From d6185220c2a226f3756ad556ad3c1a0355165884 Mon Sep 17 00:00:00 2001 From: Christine Nicole James Date: Wed, 18 Feb 2015 13:47:47 -0500 Subject: [PATCH 04/10] Script for gnuplot to plot the magnetization vs the number of iterations for all T values. --- create_mvsSteps_Plot.p | 25 +++++++++++++++++++++++++ 1 file changed, 25 insertions(+) create mode 100755 create_mvsSteps_Plot.p diff --git a/create_mvsSteps_Plot.p b/create_mvsSteps_Plot.p new file mode 100755 index 0000000..12abebf --- /dev/null +++ b/create_mvsSteps_Plot.p @@ -0,0 +1,25 @@ +reset + + +set xlabel "Millions of Steps" +set ylabel "Magnetization, m" + +set key right top +set key outside + +plot "Results1.0" using 1:2 with line title "T=1.0" +replot "Results2.0" using 1:2 with line title "T=2.0" +replot "Results2.1" using 1:2 with line title "T=2.1" +replot "Results2.2" using 1:2 with line title "T=2.2" +replot "Results2.3" using 1:2 with line title "T=2.3" +replot "Results2.4" using 1:2 with line title "T=2.4" +replot "Results2.5" using 1:2 with line title "T=2.5" +replot "Results2.6" using 1:2 with line title "T=2.6" +replot "Results2.7" using 1:2 with line title "T=2.7" +replot "Results2.8" using 1:2 with line title "T=2.8" +replot "Results2.9" using 1:2 with line title "T=2.9" +replot "Results3.0" using 1:2 with line title "T=3.0" +replot "Results4.0" using 1:2 with line title "T=4.0" +set terminal png size 400,300 enhanced font ",20" +set output "m_vs_Steps_plot.png" +replot From 0c15916826aeb4a892b1e70701625bec78ad8927 Mon Sep 17 00:00:00 2001 From: Christine Nicole James Date: Wed, 18 Feb 2015 13:48:39 -0500 Subject: [PATCH 05/10] Script for gnuplot to plot the magnetization values vs the respective T values. --- create_mvsT_Plot.p | 16 ++++++++++++++++ 1 file changed, 16 insertions(+) create mode 100755 create_mvsT_Plot.p diff --git a/create_mvsT_Plot.p b/create_mvsT_Plot.p new file mode 100755 index 0000000..0756e35 --- /dev/null +++ b/create_mvsT_Plot.p @@ -0,0 +1,16 @@ + +reset + +set xlabel "Temperature, T" +set ylabel "Magnetization, m" + +unset key + +plot "avg_m_values" lt rgb "black" with linespoints, "avg_m_values" using 1:2:3 with yerrorbars +set terminal png size 400,300 enhanced font ",20" + +set term png +set output "m_vs_T_plot.png" +replot + + From 7e8c6a4532790bd60ff812b914e4fd21b3d84685 Mon Sep 17 00:00:00 2001 From: Christine Nicole James Date: Wed, 18 Feb 2015 15:02:11 -0500 Subject: [PATCH 06/10] Latest version of ising code which runs calculations and writes results to file. --- isingCode.f95 | 33 ++++++++++++++++++++++++++++----- 1 file changed, 28 insertions(+), 5 deletions(-) diff --git a/isingCode.f95 b/isingCode.f95 index bcc5c15..c4f194f 100755 --- a/isingCode.f95 +++ b/isingCode.f95 @@ -2,6 +2,8 @@ program isingtest IMPLICIT NONE +!Definition of all varables, arrays and strings + integer :: i, j, flipSpins, k, Tstep, everyHundred integer :: size, i_swap_value, j_swap_value integer :: avgCount, mCount @@ -20,50 +22,65 @@ program isingtest character(len=7) :: out_file_base character(len=3) :: out_file_no +!Dimension of square array size=100 +!Boltzmann Constant kB=1 out_file_base="Results" open (unit=out_unit2,file="avg_m_values",action="write",status="replace") +!Loops through spin flip iterations for T=1.0 and T-2.0 do Tstep=1,2 k=1 T=Tstep beta=1/(kB*T) + +! Creates new outfile for each T with m values +! for each one hundred flips write(out_file_no,"(F3.1)") T out_file=out_file_base//out_file_no open (unit=out_unit,file=out_file,action="write",status="replace") + +!Initiate array to have every value equal to positive 1, spin up do i=1,size do j=1,size spins(i,j)=1 end do end do - + +! Resets variables m_Avg=0 everyHundred=1 avgCount=1 mCount=1 avgM=0 diffSqSum=0 + +! Iterate 5 million times, flipping a random spin each time do flipSpins=1,5000000 rand = get_random_number() +! Selects random numbers and uses to select i,j coors to +! determine which spin will be flipped rand = get_random_number() i_swap_value = get_random_whole_number(rand,size) - rand = get_random_number() j_swap_value = get_random_whole_number(rand,size) +! Flip Selected spin spins(i_swap_value, j_swap_value)=spins(i_swap_value, j_swap_value)*(-1) e_new=0 e_old=0 +! Calculate energy contribution of flipped spin in new and old state while +! accounting for periodic boundary conditions if (i_swap_value>1) then e_new=e_new+(spins(i_swap_value,j_swap_value)*spins((i_swap_value-1),j_swap_value)) e_old=e_old+(spins(i_swap_value,j_swap_value)*spins((i_swap_value-1),j_swap_value)*(-1)) @@ -93,12 +110,12 @@ program isingtest e_old=e_old+(spins(i_swap_value,j_swap_value)*spins(i_swap_value,1)*(-1)) end if +! Calculate the difference between energy values of the two states e_new=(-1)*e_new e_old=(-1)*e_old - delta_e=e_new-e_old - +! Apply Metropolis codition if (delta_e>0) then rand=get_random_number() g=exp((-beta*delta_e)) @@ -107,6 +124,7 @@ program isingtest end if end if +! Calculate and record m value every 100 steps if (everyHundred == 100) then m=0 do i=1,size @@ -123,14 +141,17 @@ program isingtest m_T(1,k)=flipSpins m_T(1,k)=m_T(1,k)/1000000.0 write (out_unit,*) m_T(1,k),m_T(2,k) - + +! If the iteration is 3 million or above use to calculate average if (flipSpins>2999999) then m_avg=m_avg+m +! Calculate average m evert 100000 spin flip iterations if (avgCount==1000) then m_avg=m_avg/avgCount avgCount=0 m_bins(mCount)=m_avg mCount=mCount+1 + m_avg=0 end if avgCount=avgCount+1 end if @@ -268,6 +289,7 @@ program isingtest avgCount=0 m_bins(mCount)=m_avg mCount=mCount+1 + m_avg=0 end if avgCount=avgCount+1 end if @@ -405,6 +427,7 @@ program isingtest avgCount=0 m_bins(mCount)=m_avg mCount=mCount+1 + m_avg=0 end if avgCount=avgCount+1 end if From 21986621093a393cebfd1222d652710137e74d99 Mon Sep 17 00:00:00 2001 From: Christine Nicole James Date: Wed, 18 Feb 2015 15:15:21 -0500 Subject: [PATCH 07/10] Latest version of ising code which runs calculations and writes results to file. --- isingCode.f95 | 26 ++++++++------------------ 1 file changed, 8 insertions(+), 18 deletions(-) diff --git a/isingCode.f95 b/isingCode.f95 index c4f194f..7f245bd 100755 --- a/isingCode.f95 +++ b/isingCode.f95 @@ -22,17 +22,17 @@ program isingtest character(len=7) :: out_file_base character(len=3) :: out_file_no -!Dimension of square array +! Dimension of square array size=100 -!Boltzmann Constant +! Boltzmann Constant kB=1 out_file_base="Results" open (unit=out_unit2,file="avg_m_values",action="write",status="replace") -!Loops through spin flip iterations for T=1.0 and T-2.0 +! Loops through spin flip iterations for T=1.0 and T-2.0 do Tstep=1,2 k=1 @@ -145,7 +145,7 @@ program isingtest ! If the iteration is 3 million or above use to calculate average if (flipSpins>2999999) then m_avg=m_avg+m -! Calculate average m evert 100000 spin flip iterations +! Calculate average m every 100,000 spin flip iterations if (avgCount==1000) then m_avg=m_avg/avgCount avgCount=0 @@ -167,6 +167,7 @@ program isingtest !Iterations end end do + mCount=mCount-1 do i=1,mCount avgM=avgM+m_bins(i) @@ -186,6 +187,7 @@ program isingtest !Temp end end do +!Loops through spin flip iterations for T=2.1-2.9 do Tstep=1,9 k=1 @@ -324,6 +326,7 @@ program isingtest !Temp end end do +!Loops through spin flip iterations for T=3.0 and T-4.0 do Tstep=3,4 k=1 @@ -497,17 +500,4 @@ function get_random_whole_number(y,x) end function -end program isingtest - - -!write (out_unit,*) spins(1,1),spins(1,2),spins(1,3),spins(1,4),spins(1,5),spins(1,6),spins(1,7),spins(1,8),spins(1,9),spins(1,10) -!write (out_unit,*) spins(2,1),spins(2,2),spins(2,3),spins(2,4),spins(2,5),spins(2,6),spins(2,7),spins(2,8),spins(2,9),spins(2,10) -!write (out_unit,*) spins(3,1),spins(3,2),spins(3,3),spins(3,4),spins(3,5),spins(3,6),spins(3,7),spins(3,8),spins(3,9),spins(3,10) -!write (out_unit,*) spins(4,1),spins(4,2),spins(4,3),spins(4,4),spins(4,5),spins(4,6),spins(4,7),spins(4,8),spins(4,9),spins(4,10) -!write (out_unit,*) spins(5,1),spins(5,2),spins(5,3),spins(5,4),spins(5,5),spins(5,6),spins(5,7),spins(5,8),spins(5,9),spins(5,10) -!write (out_unit,*) spins(6,1),spins(6,2),spins(6,3),spins(6,4),spins(6,5),spins(6,6),spins(6,7),spins(6,8),spins(6,9),spins(6,10) -!write (out_unit,*) spins(7,1),spins(7,2),spins(7,3),spins(7,4),spins(7,5),spins(7,6),spins(7,7),spins(7,8),spins(7,9),spins(7,10) -!write (out_unit,*) spins(8,1),spins(8,2),spins(8,3),spins(8,4),spins(8,5),spins(8,6),spins(8,7),spins(8,8),spins(8,9),spins(8,10) -!write (out_unit,*) spins(9,1),spins(9,2),spins(9,3),spins(9,4),spins(9,5),spins(9,6),spins(9,7),spins(9,8),spins(9,9),spins(9,10) -!write(out_unit,*)spins(10,1),spins(10,2),spins(10,3),spins(10,4),spins(10,5),spins(10,6),spins(10,7),spins(10,8),spins(10,9) -!write (out_unit,*) ' ' +end program isingtest \ No newline at end of file From 4d17ec2117666586d96ee8e59e3722856a407d74 Mon Sep 17 00:00:00 2001 From: Christine Nicole James Date: Wed, 18 Feb 2015 16:23:28 -0500 Subject: [PATCH 08/10] Script for gnuplot to plot the magnetization values vs the respective T values. --- create_mvsT_Plot.p | 10 ++++++++-- 1 file changed, 8 insertions(+), 2 deletions(-) diff --git a/create_mvsT_Plot.p b/create_mvsT_Plot.p index 0756e35..87ce1a7 100755 --- a/create_mvsT_Plot.p +++ b/create_mvsT_Plot.p @@ -1,7 +1,6 @@ - reset -set xlabel "Temperature, T" +set xlabel "k_B*T/J" set ylabel "Magnetization, m" unset key @@ -14,3 +13,10 @@ set output "m_vs_T_plot.png" replot + + + + + + + From 88c6d2ed599a464f21739be4ff7126954b5ee1f8 Mon Sep 17 00:00:00 2001 From: Christine Nicole James Date: Wed, 18 Feb 2015 21:09:02 -0500 Subject: [PATCH 09/10] Script for gnuplot to plot the magnetization vs the number of iterations for all dimensionless T values --- create_mvsSteps_Plot.p | 28 ++++++++++++++-------------- 1 file changed, 14 insertions(+), 14 deletions(-) diff --git a/create_mvsSteps_Plot.p b/create_mvsSteps_Plot.p index 12abebf..32f76cf 100755 --- a/create_mvsSteps_Plot.p +++ b/create_mvsSteps_Plot.p @@ -7,19 +7,19 @@ set ylabel "Magnetization, m" set key right top set key outside -plot "Results1.0" using 1:2 with line title "T=1.0" -replot "Results2.0" using 1:2 with line title "T=2.0" -replot "Results2.1" using 1:2 with line title "T=2.1" -replot "Results2.2" using 1:2 with line title "T=2.2" -replot "Results2.3" using 1:2 with line title "T=2.3" -replot "Results2.4" using 1:2 with line title "T=2.4" -replot "Results2.5" using 1:2 with line title "T=2.5" -replot "Results2.6" using 1:2 with line title "T=2.6" -replot "Results2.7" using 1:2 with line title "T=2.7" -replot "Results2.8" using 1:2 with line title "T=2.8" -replot "Results2.9" using 1:2 with line title "T=2.9" -replot "Results3.0" using 1:2 with line title "T=3.0" -replot "Results4.0" using 1:2 with line title "T=4.0" -set terminal png size 400,300 enhanced font ",20" +plot "Results1.0" using 1:2 with line title "kB T/J=1.0" +replot "Results2.0" using 1:2 with line title "kB T/J=2.0" +replot "Results2.1" using 1:2 with line title "kB T/J=2.1" +replot "Results2.2" using 1:2 with line title "kB T/J=2.2" +replot "Results2.3" using 1:2 with line title "kB T/J=2.3" +replot "Results2.4" using 1:2 with line title "kB T/J=2.4" +replot "Results2.5" using 1:2 with line title "kB T/J=2.5" +replot "Results2.6" using 1:2 with line title "kB T/J=2.6" +replot "Results2.7" using 1:2 with line title "kB T/J=2.7" +replot "Results2.8" using 1:2 with line title "kB T/J=2.8" +replot "Results2.9" using 1:2 with line title "kB T/J=2.9" +replot "Results3.0" using 1:2 with line title "kB T/J=3.0" +replot "Results4.0" using 1:2 with line title "kB T/J=4.0" +set terminal png size 600,300 enhanced font ",20" set output "m_vs_Steps_plot.png" replot From 9ed72f66f05d831fd8b9ccc1c28efb414af4cc8a Mon Sep 17 00:00:00 2001 From: Christine Nicole James Date: Wed, 18 Feb 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