Source Code for Program "Ising"

For use with An Introduction to Thermal Physics by Daniel V. Schroeder.

This code is written in True Basic. To learn more about this easy-to-use computer language, see the True Basic web site. To download a free student version of the True Basic compiler, click here for the Mac version or click here for the DOS version. Although there is no free version for Windows (as opposed to DOS), you can download a demo version of the low-cost Bronze Edition from the True Basic web site.

A few comments: Unlike the pseudocode in the text, this version of the program runs indefinitely until you press the mouse button. To modify it to run for a fixed number of iterations, remove the "do . . . loop" lines and the "get mouse" instruction, then change the value 100 in the "for" instruction to whatever number you like. Also note that this version prompts you for the lattice size and temperature, so you don't have to change the code every time you run the program. Feel free to change "blue" and "yellow" in the colorsquare subroutine to your two favorite colors. Enjoy!

program ising          ! Monte Carlo simulation of a 2D Ising model
                       ! using the Metropolis algorithm (importance sampling)

dim s(50,50)                        ! declare array of dipoles
input prompt "Size of lattice (max 50): ": size  
input prompt "Temperature (units of epsilon/k): ": T
set window 0,(size+2)*1.55,0,(size+2)*1.1   ! coordinates for graphics
randomize                           ! different random numbers for each run
call initialize(s,size)
do                                  ! main iteration loop
 for iteration = 1 to 100
  let i = int(rnd*size+1)           ! choose a random row number
  let j = int(rnd*size+1)           ! and a random column number
  call deltaU(s,i,j,size,Ediff)     ! compute hypothetical delta-U of flip
  if Ediff <= 0 then                ! if flipping reduces the energy...
    let s(i,j) = -s(i,j)            ! then flip it!
    call colorsquare(i,j,s(i,j))
  else
    if rnd < exp(-Ediff/T) then     ! otherwise the Boltzmann factor
      let s(i,j) = -s(i,j)          ! gives the probability of flipping
      call colorsquare(i,j,s(i,j))
    end if
  end if
 next iteration
 get mouse x,y,mousestate           ! check mouse every 100 iterations
loop until mousestate = 1
end

sub deltaU(s(,),i,j,size,Ediff)       ! compute delta-U of flipping a dipole
                                      ! (complicated because of pbc)
  if i=1 then let top = s(size,j) else let top = s(i-1,j)
  if i=size then let bottom = s(1,j) else let bottom = s(i+1,j)
  if j=1 then let left = s(i,size) else let left = s(i,j-1)
  if j=size then let right = s(i,1) else let right = s(i,j+1)
  let Ediff = 2*s(i,j)*(top+bottom+left+right)
end sub

sub initialize(s(,),size)             ! initialize to random array
  for i = 1 to size
    for j = 1 to size
      if rnd < .5 then let s(i,j) = 1 else let s(i,j) = -1
      call colorsquare(i,j,s(i,j))
    next j
  next i
end sub

sub colorsquare(i,j,s)                ! color square i,j according to s
  if s = 1 then set color "blue" else set color "yellow"
  box area i,i+1,j,j+1
end sub

Last modified on September 22, 2000.