Hans-Otto Georgii:

"Perfect" simulation of the continuum Ising model

The model consists of point particles of two types with soft-core intertype repulsion. There are two parameters: z > 0, the activity, which governs the particle density, and ß > 0, the inverse temperature.
The simulations use a Propp-Wilson-variant of a Gibbs sampler.
For more mathematical background see Section 4.4 of this paper (ps-file) .


Download of a Macintosh application

(for system requirements and description click here)


Some pictures:

The repulsive intertype potential is J(x-y)= (1-|x-y|)^2 for |x-y|<=1.
The linear size of the window is L= 20 .
Outside of the window is a boundary condition consisting of a Poisson crowd of white particles.

Subcritical case

  • z = 4, ß = 3 : particle picture  /  random cluster representation
  • Supercritical case

  • z = 4.5, ß = 3 : particle picture  /  random cluster representation

  • z = 4, ß = 4 : particle picture  /  random cluster representation


  • Link to David Wilson's webpage on perfect simulation