Ising Model for Ferromagnetism

• Jonathan V. Selinger
  • 1
  Email author

1. 1.Chemical Physics Interdisciplinary ProgramLiquid Crystal Institute, Kent State UniversityKentUSA

Chapter

First Online: 20 August 2015

Abstract

This chapter presents the Ising model for ferromagnetism, which is a standard simple model of a phase transition. Using the approximation of mean-field theory , the free energy is minimized, and hence the magnetization is calculated, as a function of temperature and applied field. This calculation demonstrates some fundamental concepts in statistical mechanics, including spontaneous symmetry breaking , an order parameter with magnitude and direction, first- and second-order phase transitions, and a critical point characterized by critical exponents . In the rest of the book, these concepts will be applied to the theory of soft matter.

https://sci-hub.tw/10.1007/978-3-319-21054-4_2

From the book: Introduction to the Theory of Soft Matter: From Ideal Gases to Liquid Crystals

  Wilhelm Lenz     Ernst Ising