Monte Carlo method on a 2D Ising Lattice of Spins

by Kenji Harada

Introduction

This java applet demonstrates three algorithms applied to the Ising model : Metropolis's method[1], Swendsen and Wang's algorithm[2] and Wolff's algorithm[3]. Metropolis's algorithm is called a single spin flip algorithm. SW and Wolff's algorithm are called cluster algorithms. Cluster algorithms can dramatically reduce the effects of critical slowing down and have been applied to many models.

[1] N.Metropolis, A.W.Rosenbluth,M.N.Rosenbluth,A.H.Teller,E.Teller, J.Chem.Phys. 21,1087 (1953).
[2] R.H.Swendsen and J.-S.Wang, Phys.Rev.Lett. 58, 86 (1987).
[3] U.Wolff, Phys.Rev.Lett. 62,361 (1989).

Description of this applet

Center panel is a lattice, its size is 32x32. Spin's colors are red and white. Black lines in the center panel is the boundary of the cluster. The right pole is a temperature meter, it's unit is Tc=2/ln(1+sqrt 2). You can change temparature , when you click the mouse button on the meter. (This is the source code) 
Button:  "Change"  Change algorithm!   "Run"     Auto mode ON.
         "Stop"    Auto mode OFF.      "Step"    Go 1 step!

Any comment you could give me would be much appreciated.
My e-mail address : harara@kuamp.kyoto-u.ac.jp