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Journal of Physics A Mathematical and General

Quantum N-colour Ashkin-Teller model: exact solution in the large-N limit

Hermenegildo Alejandro Ceccatto

Published Jun 21, 1991• 8 citations
Publisher

Abstract

The statistical mechanics of the quantum N-colour Ashkin-Teller model is solved exactly in the large-N limit. It is shown that the results can be expressed in terms of the partition function of some effective Ising model in a transverse field. The structure of the ground state is found to be equivalent to the phase diagram of the classical system.

DOI
10.1088/0305-4470/24/12/021

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Journal of Experimental and Theoretical Physics Letters•Jul 1, 2003•5 citations
The statistical mechanics of the quantum N-colour Ashkin-Teller model is solved exactly in the large-N limit. It is shown that the results can be expressed in terms of the partition function of some effective Ising model in a transverse field. The structure of the ground state is found to be equivalent to the phase diagram of the classical system.
The NNN-color Ashkin-Teller model is solved exactly in the large-NNN limit in two dimensions. The phase diagram is found. It is shown that for positive four-spin coupling the transition is first order while for negative four-spin coupling the transition is continuous and Ising type. The specific heat near the second-order transition is calculated and it is found to be finite at the transition because of large corrections to scaling. The latent heat and correlation length at the first-order transition are also calculated.
Magnetic properties and phase diagrams of a spin-1/2 anisotropic Ashkin-Teller model in a transverse field are studied using the mean field theory. On the one hand, it is found that there exists a critical value of the transverse field Ωc/J1 above which the partially ordered phase 〈σS〉 appears at very low temperature and sufficiently large values of the four-spin interaction coefficient J4/J1. Such result is not obtained in the Ω/J1 = 0 case. On the other hand, the multicritical behaviour is also studied as a function of the transverse field Ω/J1 for selected values of the spin interaction coefficient J2/J1. However, depending on the transverse field value, and a fixed J2/J1 value, four varieties of phase diagrams are found. General formulae are established for an arbitrary coordination number q. The phase diagrams and the behaviour of the transverse and longitudinal magnetisations are given for q = 4.
The generalized Ashkin-Teller model involving both biquadratic and bilinear interactions between the Ising subsystems (α and s ) and equivalent to the anisotropic Ising model with spin 3/2 is considered. For a certain magnitude of the opposite-sign bilinear interactions along the horizontal and vertical axes of a square lattice, the exact analytic solution is obtained that describes the phase transition between the disordered (〈α 〉=〈 s 〉=〈α s 〉=0) and the correlated ordered (〈 s 〉 ≠0 and 〈α〉=〈 s 〉=0) states.