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Journal of Physics A Mathematical and General

Phase diagram and critical properties of the (1+1)-dimensional Ashkin-Teller model

Ferenc Iglói, Jenő Sólyom

Published May 11, 1984• 22 citations
Publisher

Abstract

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.

DOI
10.1088/0305-4470/17/7/021

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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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We investigate the boundary critical phenomena of the one-dimensional quantum Ashkin-Teller model using boundary conformal field theory and density matrix renormalization group (DMRG) simulations. Based on the Z2\mathbb{Z}_2Z2​-orbifold of the c=1c=1c=1 compactified boson boundary conformal field theory, we construct microscopic lattice boundary terms that renormalize to the stable conformal boundary conditions, utilizing simple current extensions and the underlying SU(2)\mathrm{SU}(2)SU(2) symmetry to explicitly characterize the four-state Potts point. We validate these theoretical identifications via finite-size spectroscopy of the lattice energy spectra, confirming their consistency with D4D_4D4​ symmetry and Kramers-Wannier duality. Finally, we discuss the boundary renormalization group flows among these identified fixed points to propose a global phase diagram for the boundary criticality.
A real-space rescaling technique (decimation) is used to study the critical properties of the bond-dilute, S state Ashkin-Teller-Potts model on the square lattice. Fixed points and critical exponents are obtained and critical curves plotted for values of S from 1 to 4. For S=1, 2 the dilute model exhibits the same critical behaviour as the pure system. However, for S=3, 4, there is crossover to a new dilute fixed point. The transition remains second order but exhibits new values of the critical exponents. This behaviour is in accord with the Harris criterion (1974).