For use with An Introduction to Thermal Physics by Daniel V. Schroeder.
This code is written in Java (version 1.1). You can copy the code below and paste it into a file (call the file "Ising.java"), or click here to download a ready-to-compile copy in a separate file.
If you don't like Java, click here for a list of versions of the Ising program in other languages. (All the others run much slower than the Java version, so they're not suitable for simulating large lattices.)
To compile and run this program, you must have the Java Development Kit (JDK) installed on your computer. If you don't already have the JDK, you can download it (free!) from Oracle's web site. Be sure to read the installation instructions carefully.
Once you have Java installed, and you have set the PATH variable if necessary, just open a Terminal or Command Prompt window and cd to the directory containing the Ising.java file. Then type "javac Ising.java" to compile, and "java Ising" to run the program.
Much of the clutter in the code below is to set up the GUI, which includes a start/pause button and a slider to adjust the temperature. The physics code is in the run and deltaU methods.
This program runs pretty quickly on modern computers, but further optimizations are possible. You could add an option to turn off the graphics temporarily, and/or use a MemoryImageSource to speed up the graphics.
import java.awt.*;
import java.awt.event.*;
import java.text.DecimalFormat;
class Ising extends Canvas implements Runnable {
int size = 100; // number of lattice sites in a row (change if desired)
int squareWidth = 5; // pixels across one lattice site (change if desired)
int canvasSize = size * squareWidth; // total pixels across canvas
int[][] s = new int[size][size]; // the 2D array of dipoles (each equal to 1 or -1)
boolean running = false; // true when simulation is running
Button startButton = new Button(" Start ");
Scrollbar tScroller; // scrollbar to adjust temperature
Label tLabel = new Label("Temperature = 2.27 "); // text label next to scrollbar
DecimalFormat twoPlaces = new DecimalFormat("0.00"); // to format temperature readout
Image offScreenImage; // for double-buffering
Graphics offScreenGraphics;
Color upColor = new Color(100,0,255); // purple
Color downColor = new Color(255,255,255); // white
// Constructor method handles all the initializations:
Ising() {
Frame isingFrame = new Frame("Ising Model"); // initialize the GUI...
isingFrame.addWindowListener(new WindowAdapter() {
public void windowClosing(WindowEvent e) {
System.exit(0); // close button exits program
}
});
Panel canvasPanel = new Panel();
isingFrame.add(canvasPanel);
canvasPanel.add(this);
setSize(canvasSize,canvasSize);
Panel controlPanel = new Panel();
isingFrame.add(controlPanel,BorderLayout.SOUTH);
controlPanel.add(tLabel);
tScroller = new Scrollbar(Scrollbar.HORIZONTAL,227,1,1,1001) {
public Dimension getPreferredSize() {
return new Dimension(100,15); // make it bigger than default
}
};
tScroller.setBlockIncrement(1); // enables fine adjustments in Mac OS X 10.7+
tScroller.addAdjustmentListener(new AdjustmentListener() {
public void adjustmentValueChanged(AdjustmentEvent e) {
tLabel.setText("Temperature = " + twoPlaces.format(tScroller.getValue()/100.0));
}
});
controlPanel.add(tScroller);
controlPanel.add(new Label(" ")); // leave some space
startButton.addActionListener(new ActionListener() {
public void actionPerformed(ActionEvent e) {
running = !running;
if (running) startButton.setLabel("Pause"); else startButton.setLabel("Resume");
}
});
controlPanel.add(startButton);
isingFrame.pack();
offScreenImage = createImage(canvasSize,canvasSize);
offScreenGraphics = offScreenImage.getGraphics();
for (int i=0; i < size; i++) { // initialize the lattice...
for (int j=0; j < size; j++) {
if (Math.random() < 0.5) s[i][j] = 1; else s[i][j] = -1;
colorSquare(i,j);
}
}
isingFrame.setVisible(true); // we're finally ready to show it!
Thread t = new Thread(this); // create a thread to run the simulation
t.start(); // and let 'er rip...
}
// Run method gets called by new thread to carry out the simulation:
public void run() {
while (true) {
if (running) {
double temp = tScroller.getValue() / 100.0;
for (int step=0; step<10000; step++) { // adjust number of steps as desired
int i = (int) (Math.random() * size); // choose a random row and column
int j = (int) (Math.random() * size);
double eDiff = deltaU(i,j); // compute energy change if flipped
if ((eDiff <= 0) || (Math.random() < Math.exp(-eDiff/temp))) { // Metropolis!
s[i][j] *= -1;
colorSquare(i,j);
}
}
repaint(); // causes update method to be called soon
}
try { Thread.sleep(1); } catch (InterruptedException e) {} // sleep time in milliseconds
}
}
// Given a lattice site, compute energy change from hypothetical flip; note pbc:
double deltaU(int i, int j) {
int leftS, rightS, topS, bottomS; // values of neighboring spins
if (i == 0) leftS = s[size-1][j]; else leftS = s[i-1][j];
if (i == size-1) rightS = s[0][j]; else rightS = s[i+1][j];
if (j == 0) topS = s[i][size-1]; else topS = s[i][j-1];
if (j == size-1) bottomS = s[i][0]; else bottomS = s[i][j+1];
return 2.0 * s[i][j] * (leftS + rightS + topS + bottomS);
}
// Color a given square according to the site's orientation:
void colorSquare(int i, int j) {
if (s[i][j] == 1) offScreenGraphics.setColor(upColor);
else offScreenGraphics.setColor(downColor);
offScreenGraphics.fillRect(i*squareWidth,j*squareWidth,squareWidth,squareWidth);
}
// Override default update method to skip drawing the background:
public void update(Graphics g) {
paint(g);
}
// Paint method just blasts the off-screen image to the screen:
public void paint(Graphics g) {
g.drawImage(offScreenImage,0,0,canvasSize,canvasSize,this);
}
// Main method just calls constructor to get started:
public static void main(String[] args) {
new Ising();
}
}
Last modified on January 20, 2013.