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1984•Physical Review LettersRequires access

Exact Results for Two- and Three-Dimensional Ising and Potts Models

Eytan Domany

Open publisher page 93 citations

Abstract

The exact transition temperature, as well as some of the critical exponents, of certain three-dimensional Ising and Potts models is presented. With the analytic results supplemented by assumptions concerning the validity of universality, the critical point is identified as a Liftshitz point. On the basis of hyperscaling, the dynamic exponent $z$ for two-dimensional Ising and Potts model is predicted to be given by $z\ensuremath{\nu}=2+\ensuremath{\alpha}$.

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What this paper is about

The exact transition temperature, as well as some of the critical exponents, of certain three-dimensional Ising and Potts models is presented. With the analytic results supplemented by assumptions concerning the validity of universality, the critical point is identified as a Liftshitz point. On the basis of hyperscaling, the dynamic exponent $z$ for two-dimensional Ising and Potts model is predicted to be given by $z\ensuremath{\nu}=2+\ensuremath{\alpha}$.

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OpenAlex reports 93 citations for this work. Citation counts describe recorded attention and do not establish research quality.

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Available abstract

The exact transition temperature, as well as some of the critical exponents, of certain three-dimensional Ising and Potts models is presented. With the analytic results supplemented by assumptions concerning the validity of universality, the critical point is identified as a Liftshitz point. On the basis of hyperscaling, the dynamic exponent $z$ for two-dimensional Ising and Potts model is predicted to be given by $z\ensuremath{\nu}=2+\ensuremath{\alpha}$.

Key concepts: Potts model, Ising model, Chiral Potts curve, Universality (dynamical systems), Critical exponent, Critical point (mathematics), Statistical physics, Exponent

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