For use with An Introduction to Thermal Physics by Daniel V. Schroeder.
This code is written in Python, using the widely available Tkinter module for graphics and GUI controls. If you don't already have Python installed, I recommend the EPD Free distribution from Enthought.
If you don't like Python or Tkinter, click here for a list of versions of the Ising program in other languages (including Visual Python).
# ising.py
# Simulates the two-dimensional Ising model using the Metropolis algorithm
# This version uses Tkinter for the GUI
# By Dan Schroeder, Weber State University, January 2013
import Tkinter, numpy, random, math
size = 50 # number of sites in a lattice row (change if desired)
squareWidth = 10 # width of one site in pixels (change if desired)
canvasWidth = size * squareWidth # full width of canvas in pixels
s = numpy.ones((size, size), int) # 2D array of dipoles (1=up, -1=down)
running = False # will be true when simulation is running
theWindow = Tkinter.Tk() # create the GUI window
theWindow.title("Ising Model")
theWindow.geometry('+50+50') # get the window away from the corner
# Here's the Canvas where we draw the lattice using a Tkinter PhotoImage:
theCanvas = Tkinter.Canvas(theWindow, width=canvasWidth, height=canvasWidth)
theCanvas.pack() # put it at the top of the window
theImage = Tkinter.PhotoImage(width=canvasWidth, height=canvasWidth)
theCanvas.create_image((3, 3), image=theImage, anchor="nw", state="normal")
# The coordinates (3, 3) are a kludge to eliminate a mysterious offset that occurs otherwise.
# Function called when Start/Stop button is pressed:
def startStop():
global running
running = not running
if running:
goButton.config(text="Pause")
else:
goButton.config(text="Resume")
# Create the GUI controls:
controlFrame = Tkinter.Frame(theWindow) # a frame to hold the GUI controls
controlFrame.pack() # put it below the canvas
tLabel = Tkinter.Label(controlFrame, text="Temperature: ")
tLabel.pack(side="left")
tSlider = Tkinter.Scale(controlFrame, from_=0.01, to=10.0, resolution=0.01, length=120, orient="horizontal")
tSlider.pack(side="left")
tSlider.set(2.27) # set to critical temperature initially
spacer = Tkinter.Frame(controlFrame, width=40)
spacer.pack(side="left")
goButton = Tkinter.Button(controlFrame, text="Start", width=8, command=startStop)
goButton.pack(side="left")
# Function to color the square representing site (i,j):
def colorSquare(i, j):
theColor = "#7000ff" if s[i,j]==1 else "#ffffff" # purple and white
theImage.put(theColor, to=(i*squareWidth,j*squareWidth,(i+1)*squareWidth,(j+1)*squareWidth))
# the "put" function colors the indicated rectangle within the image
# Function to calculate energy change upon hypothetical flip (with pbc):
def deltaE(i,j):
leftS = s[size-1,j] if i==0 else s[i-1,j]
rightS = s[0,j] if i==size-1 else s[i+1,j]
topS = s[i,size-1] if j==0 else s[i,j-1]
bottomS = s[i,0] if j==size-1 else s[i,j+1]
return 2.0 * s[i,j] * (leftS + rightS + topS + bottomS)
# Main simulation "loop" schedules a call to itself upon completion:
def simulate():
if running:
T = tSlider.get() # get the current temperature
for step in range(1000): # (change the number of steps as desired)
i = int(random.random()*size) # choose a random row and column
j = int(random.random()*size)
eDiff = deltaE(i,j)
if eDiff <= 0 or random.random() < math.exp(-eDiff/T): # Metropolis!
s[i,j] = -s[i,j]
colorSquare(i, j)
theWindow.after(1,simulate) # come back in one millisecond
# Initialize to a random array, and draw it as we go:
for i in range(size):
for j in range(size):
s[i,j] = 1 if random.random()<0.5 else -1
colorSquare(i,j)
simulate() # start the simulation!
theWindow.mainloop() # start the GUI event loop
Last modified on January 20, 2013.