# 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

Statistical Mechanics I TOC

Overview TOC

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