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Journal of Physics A Mathematical and General

Unusual phase properties of the ZN-symmetric quartet FCC model

Francisco Castilho Alcaraz, L Jacobs, Robert S. Savit

Published Jan 11, 1983• 2 citations
Publisher

Abstract

A Z N -symmetric theory with four-spin interactions on a three-dimensional FCC lattice is analysed. The model possesses an unusual semi-local symmetry and is self-dual. For N<N c approximately=5 it undergoes a single, first-order transition, whereas for N>or=N c it exhibits two continuous transitions which may or may not be infinite order. The intermediate phase appearing between the ferromagnetic ordered and disordered phases for N>or=N c is a massless phase with no long-range order. The behaviour of the theory is strongly reminiscent of that of the two-dimensional Z N spin models and the four-dimensional Z N gauge theories and, quite naturally, constitutes a three-dimensional interpolating model. The possible relevance of this and related models to the Lifshitz point problem in certain helical magnetic and liquid crystal systems is briefly discussed.

DOI
10.1088/0305-4470/16/1/025

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Self-dual S3S_3S3​-invariant quantum chains
We investigate the self-dual three-state quantum chain with nearest-neighbor interactions and S_3 S 3 , time-reversal, and parity symmetries. We find a rich phase diagram including gapped phases with order-disorder coexistence, integrable critical points with U(1) U ( 1 ) symmetry, and ferromagnetic and antiferromagnetic critical regions described by three-state Potts and free-boson conformal field theories respectively. We also find an unusual critical phase which appears to be described by combining two conformal field theories with distinct “Fermi velocities”. The order-disorder coexistence phase has an emergent fractional supersymmetry, and we find lattice analogs of its generators.
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