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The Ising Model

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Book cover The Theory of Magnetism II

Part of the book series: Springer Series in Solid-State Sciences ((SSSOL,volume 55))

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Abstract

In this prototype theory of ferromagnetism—and of many other physical phenomena as well—a spin Si =±1 is assigned to each of N sites on a fixed lattice. The spins, which live on the vertices of the lattice, interact with one another by means of bonds (the links of the lattice). These have strengths Jij in energy units. In addition, the spins can interact with external fields Bi of arbitrary strengths. The total energy is then given by:

$$H = - \sum {{J_{ij}}} {S_i}{S_j} - \sum {{B_i}} {S_i}$$

and can be directly evaluated in any of the 2N spin configurations. In the most familiar version of the Ising model, the interactions are limited to nearest-neighbors on the lattice and the magnetic field is homogeneous, Bi =constant.

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Authors and Affiliations

  1. Physics Department, University of Utah, 84112, Salt Lake City, UT, USA

    Professor Daniel C. Mattis Ph. D.

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  1. Professor Daniel C. Mattis Ph. D.
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© 1985 Springer-Verlag Berlin Heidelberg

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Mattis, D.C. (1985). The Ising Model. In: The Theory of Magnetism II. Springer Series in Solid-State Sciences, vol 55. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-82405-0_3

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  • DOI: https://doi.org/10.1007/978-3-642-82405-0_3

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-82407-4

  • Online ISBN: 978-3-642-82405-0

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