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1988•International Journal of Modern Physics BRequires access

SERIES ANALYSIS OF Q-STATE CHECKERBOARD POTTS MODELS

David Hansel, J.-M. Maillard

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Abstract

The series analysis of the low temperature expansion of the checkerboard q-state Potts model in a magnetic field initiated in two previous papers is continued. In particular algebraic varieties of the parameter space (corresponding or generalizing the so-called disorder solutions), the checkerboard Potts model and its Bethe approximation are indistinguishable as far as one is concerned with the partition function and its first order derivatives. The difference between the two models occurs for higher order derivatives. In particular one gives the exact expression of the (low temperature expansion of the) susceptibility of the checkerboard Ising model in zero magnetic field on one of these varieties.

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What this paper is about

The series analysis of the low temperature expansion of the checkerboard q-state Potts model in a magnetic field initiated in two previous papers is continued. In particular algebraic varieties of the parameter space (corresponding or generalizing the so-called disorder solutions), the checkerboard Potts model and its Bethe approximation are indistinguishable as far as one is concerned with the partition function and its first order derivatives. The difference between the two models occurs for higher order derivatives. In particular one gives the exact expression of the (low temperature expansion of the) susceptibility of the checkerboard Ising model in zero magnetic field on one of these varieties.

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Available abstract

The series analysis of the low temperature expansion of the checkerboard q-state Potts model in a magnetic field initiated in two previous papers is continued. In particular algebraic varieties of the parameter space (corresponding or generalizing the so-called disorder solutions), the checkerboard Potts model and its Bethe approximation are indistinguishable as far as one is concerned with the partition function and its first order derivatives. The difference between the two models occurs for higher order derivatives. In particular one gives the exact expression of the (low temperature expansion of the) susceptibility of the checkerboard Ising model in zero magnetic field on one of these varieties.

Key concepts: Checkerboard, Potts model, Chiral Potts curve, Partition function (quantum field theory), Ising model, Series (stratigraphy), Series expansion, Mathematics

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