IsingModels.jl Documentation

A simple Julia package to simulate the Ising model in a two-dimensional rectangular grid.

Package Features

• Monte Carlo samplers for the 2D Ising model: Metropolis and Wolff.
• Compute and track energy, magnetization, and configurations during a simulation.
• Analytical magnetization and critical temperature found by Onsager, as well as other analytical quantities.
• A Metropolis+F(M) sampler, where we can add an arbitrary function of the magnetization to the energy.

Outline

• IsingModels.jl Documentation
• • Package Features
  • Outline
  • Index
• The 2-dimensional Ising model
• Examples using hybrid (Metropolis + Wolff) sampling method
• • Magnetization as a function of temperature
  • Wolff steps are mixed with Metropolis steps
  • Magnetic susceptibility
  • Heat capacity
  • Wolff vs. Metropolis spin flip rates
• Examples using Wolff cluster sampling method
• • Magnetization as a function of temperature
  • Typical Wolff clusters at criticality
  • Average size of Wolff's clusters as a function of temperature
  • Wolff explores configurations efficiently at the critical temperature
  • Binder's parameter
  • Heat capacity vs. exact expression
  • Internal energy vs. exact expression
• Reference

Index