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Journal of Physics A Mathematical and General

Mean-field renormalisation group approach for the axial next-nearest-neighbour Ising model

E. C. Valadares, J. A. Plascak

Published Oct 1, 1987• 5 citations
Publisher

Abstract

The critical properties of the axial next-nearest-neighbour Ising (ANNNI) model are investigated by using the mean-field renormalisation group approach. Linear and double chain clusters lying along the axial direction are considered. Phase diagrams for the model in two and three dimensions and estimates of thermal exponents are obtained.
DOI
10.1088/0305-4470/20/14/033

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The mean-field phase diagram of a three-dimensional axial-next-nearest-neighbor Ising (ANNNI) model in a transverse field has been studied here. The dynamical modes are found by using the random-phase approximation and the phase diagram is also obtained from the softening condition of these modes. For a one-dimensional ANNNI model in a transverse field, these dynamical modes are obtained here more accurately using a Jordan-Wigner-type transformation (with some approximations). Softening of these modes gives the zero-temperature phase diagram in one dimension.
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The axial next-nearest-neighbour Ising (or ANNNI) model and the four-state asymmetric clock model both exhibit a decoupling multicritical point where they decompose into two uncoupled Ising models at criticality. The corresponding scaling exponents for various operators are given generally, the leading modulation or chiral crossover exponent being phi = gamma - nu , where gamma and nu are the pure Ising susceptibility and correlation exponents. Implications for the ANNNI model phase diagrams are discussed. Crossover scaling forms appropriate to logarithmic and marginal behaviour, with non-universal exponents, are presented.