# Chapter 5: Magnetic Systems

We apply the tools of statistical mechanics to magnetic systems. The most important and simplest model containing interactions, is the Ising model defined by the energy of a microstate $$E = -J \sum_{\lt ij \gt} s_i s_j - H \sum_i s_i,$$ where $J$ is the energy of interaction and is positive for a ferromagnetic interaction, $s_i = \pm 1$ is the spin of a spin 1/2 particle such as an electron, $\lt ij \gt$ denotes nearest-neighbor pairs of spins located on a lattice, and $H$ is the applied external magnetic field.

In addition to studying the Ising model and its variations, we consider various techniques such as transfer matrices, mean-field theories, and computer simulations, which have become essential for our understanding of magnetic systems.

## Programs

- Program 5.1: Ising 1d
- Program 5.2: Ising 2d
- Program 5.3: Ising Mean Field
- Program 5.4: Ising Hysteresis
- Program 5.5: Ising Number Of States
- Program 5.6: Potts Number Of States
- Program 5.7: Lattice Gas
- Program 5.8: Ising Antiferromagnet
- Program 5.9: Frustration