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Physical review. B, Condensed matter

Critical behavior of the n -component cubic model and the Ashkin-Teller fixed line

Bernard Nienhuis, Eberhard K. Riedel, Michael Schick C

Published May 1, 1983• 71 citations
Publisher

Abstract

The cubic lattice gas, a generalization of the $n$-component face-cubic model, is studied in two dimensions by variational renormalization-group techniques for general $n$, and by an exact mapping onto a solid-on-solid model for $n=2$. This approach reveals new interconnections among the class of cubic, Potts, and Ashkin-Teller phase-transition phenomena. In particular, it is shown that the fixed line of the Ashkin-Teller lattice gas serves as the backbone for a hierarchy of pairs of fixed points which branch off from it, as $n$ is decreased from 2, at special points where two operators are marginal. The phase diagrams of the pure and dilute $n$-component cubic models are obtained and the orders of all transitions are determined. The cubic phase transition is found to be first order for all $n>{n}_{c}=2$. The evolution of the results as a function of dimensionality is discussed briefly.

DOI
10.1103/physrevb.27.5625

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The (1+1)-dimensional Ashkin-Teller model is studied by the renormalisation group method and by the finite lattice extrapolation technique. The possible phases and their boundaries in an extended space of couplings are determined from the degeneracy structure of the low-lying levels in the thermodynamic limit. The critical behaviour is investigated for ferromagnetic couplings using increasing block sizes in the renormalisation transformation. The line of fixed points and its bifurcation at the Potts fixed point is studied.
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