Renormalization-group theory of the Heisenberg model in d dimensions

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2022

Authors

Berker, Ahmet Nihat
Berker, A. Nihat

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Elsevier

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Abstract

The classical Heisenberg model has been solved in spatial d dimensions, exactly in d = 1 and by the Migdal-Kadanoff approximation in d > 1, by using a Fourier-Legendre expansion. The phase transition temperatures, the energy densities, and the specific heats are calculated in arbitrary dimension d. Fisher's exact result is recovered in d = 1. The absence of an ordered phase, conventional or algebraic (in contrast to the XY model yielding an algebraically ordered phase) is recovered in d = 2. A conventionally ordered phase occurs at d > 2. This method opens the way to complex-system calculations with Heisenberg local degrees of freedom.(c) 2022 Elsevier B.V. All rights reserved.

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Keywords

Hierarchical Lattices, Phase-Transitions, Migdal-Kadanoff, Potts Models, Spin Systems, Field, Hierarchical Lattices, Phase transitions, Phase-Transitions, Spin models, Migdal-Kadanoff, Free energy, Potts Models, Internal energy, Spin Systems, Specific heat, Field, Renormalization-group theory

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2

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Q2

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Q2

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Physica A-Statistical Mechanics and Its Applications

Volume

608

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