The EJS 2D Ising model displays a lattice of spins. You can change the lattice size, temperature, and external magnetic field. You can modify this simulation if you have Ejs installed by right-clicking within the plot and selecting “Open Ejs Model” from the pop-up menu item. The 2D-Ising model was created using the Easy Java Simulations (Ejs) modeling tool. It is distributed as a ready-to-run (compiled) Java archive. Double clicking the ejs_stp_Ising2D.jar file will run the program if Java is installed. Ejs is a part of the Open Source Physics Project and is designed to make it easier to access, modify, and generate computer models. Additional Ejs models are available. They can be found by searching ComPADRE for Open Source Physics, OSP, or Ejs.

The STP 1DIsing program is a Monte Carlo simulation of a one-dimensional Ising model in equilibrium with a heat bath at temperature T using the Metropolis algorithm. The default is N=64 spins up (s = 1) with no external field with heat bath temperature T=1. STP Ising1D is part of a suite of Open Source Physics programs that model aspects of Statistical and Thermal Physics (STP). The program is distributed as a ready-to-run (compiled) Java archive. Double clicking the stp_Ising1D.jar file will run the program if Java is installed on your computer. Additional programs can be found by searching ComPADRE for Open Source Physics, STP, or Statistical and Thermal Physics.

The STP Ising2D program is a Monte Carlo simulation of a two-dimensional Ising model in equilibrium with a heat bath at temperature T using the Metropolis or Wolff algorithms. The default is a lattice of linear dimension L=32 (for a total of N=L^2 spins) with no external field and heat bath temperature T=0. STP Ising2D is part of a suite of Open Source Physics programs that model aspects of Statistical and Thermal Physics (STP). The program is distributed as a ready-to-run (compiled) Java archive. Double clicking the stp_Ising2D.jar file will run the program if Java is installed on your computer. Additional programs can be found by searching ComPADRE for Open Source Physics, STP, or Statistical and Thermal Physics.

The STP IsingLatticeGas program is a Monte Carlo simulation of a two-dimensional lattice gas with two halves at different chemical potentials to show diffusive equilibrium. The default is a grid of linear dimension L=32 (for a total of N=L^2 particles) and temperature T=1. The left side has a chemical potential of -1 and particle density of 0.2, and the right side has a chemical potential of -2 and a particle density of 0.04. STP IsingLatticeGas is part of a suite of Open Source Physics programs that model aspects of Statistical and Thermal Physics (STP). The program is distributed as a ready-to-run (compiled) Java archive. Double clicking the stp_IsingLatticeGas.jar file will run the program if Java is installed on your computer. Additional programs can be found by searching ComPADRE for Open Source Physics, STP, or Statistical and Thermal Physics.

We apply the general formalism of statistical mechanics developed in Chapter 4 to the Ising model, a model magnetic system for which the interactions between the magnetic moments are important. We will discover that these interactions lead to a wide range of phenomena, including the existence of phase transitions and other cooperative phenomena. Computer simulation methods will be used extensively and a simple approximation method known as mean-field theory will be introduced. The simulations can be found by searching ComPADRE for Open Source Physics, STP, or Statistical and Thermal Physics.

We first discuss a phenomenological mean-field theory of phase transitions due to Landau and introduce the ideas of universality and scaling near critical points. The breakdown of mean-field theory near a critical point leads us to introduce the renormalization group, which has had a major impact on our understanding of phase transitions, quantum field theory, and turbulence. We introduce the renormalization group in the context of percolation, a simple geometrical model that exhibits a continuous transition, and then apply renormalization group methods to the Ising model.

This web site is designed to support the effective teaching of statistical and thermal physics at the undergraduate and graduate levels. It includes simulations of the properties of standard systems and models used in thermal physics classes. Also available are lecture notes, a listing of textbooks, and links to a range of other resources. This project is a collaborative open source development of thermal physics curriculum.

The Wang-Landau algorithm, also called the flat-histogram algorithm, can be used to calculate the density of states of a microscopic system. In this simulation, the Wang-Landau algorithm is used to calculate the density of states for a two-dimensional Ising ferromagnet with periodic boundary conditions. From the density of states, the entropy, internal energy, and heat capacity are calculated as a function of temperature. You can modify this simulation if you have EJS installed by right-clicking within a plot and selecting "Open Ejs Model" from the pop-up menu item. The Wang-Landau simulation of the 2D Ising Model in Zero Field Model was developed using the Easy Java Simulations (EJS) modeling tool. It is distributed as a ready-to-run (compiled) Java archive. Double clicking the ejs_WangLandau_Ising_2D_Ferromagnet.jar file will run the program if Java is installed.