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Advanced studies in pure mathematics

Fermion Representations for the 2D and 3D Ising Models

VI. S. Dotsenko, A. M. Polyakov

Published Jun 17, 2018• 7 citations
Publisher

Abstract

Fermion variables are constructed for the 3D Ising Model in which it becomes a theory of free fermion strings defined on lattice.§ 1. Introduction
DOI
10.2969/aspm/01610171

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The two{dimensional (2D) Ising model is reviewed as a theory of free fermions on a lattice.The discussion includes the fermionization procedure based on the mirror{ordered factorization of the density matrix, Gaussian fermionic integral representation for partition function, the momentum{ space analysis and Onsager's result, the eective continuum{limit eld theories and the critical{ point singularities.The emergence of long{range fermionic correlations in a nonzero magnetic eld and the behaviour of the speci c heat along the critical isotherm are commented.Attention is given to the choice of rational computational devices.