A Continuum Generalization of the Ising Model

Haley A. Yaple; Daniel M. Abrams

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arXiv · 1306.3528

A Continuum Generalization of the Ising Model

Haley A. Yaple·Daniel M. Abrams

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Abstract

The Lenz-Ising model has served for almost a century as a basis for understanding ferromagnetism, and has become a paradigmatic model for phase transitions in statistical mechanics. While retaining the Ising energy arguments, we use techniques previously applied to sociophysics to propose a continuum model. Our formulation results in an integro-differential equation that has several advantages over the traditional version: it allows for asymptotic analysis of phase transitions, material properties, and the dynamics of the formation of magnetic domains.

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Haley A. Yaple, Daniel M. Abrams. 2013-06-14. A Continuum Generalization of the Ising Model. https://arxiv.org/abs/1306.3528

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