The Ashkin-Teller (AT) model is a generalization of Ising 2-d to a four states spin model; it can be written in the form of two Ising layers (in general with different couplings) interacting via a four-spin interaction. It was conjectured long ago (by Kadanoff and Wegner, Wu and Lin, Baxter and others) that AT has in general two critical points, and that universality holds, in the sense that the critical exponents are the same as in the Ising model, except when the couplings of the two Ising layers are equal (isotropic case). We obtain an explicit expression for the specific heat from which we prove this conjecture in the weakly interacting case and we locate precisely the critical points. We find the somewhat unexpected feature that, despite universality, holds for the specific heat, nevertheless nonuniversal critical indexes appear: for instance the distance between the critical points rescale with an anomalous exponent as we let the couplings of the two Ising layers coincide (isotropic limit); and so does the constant in front of the logarithm in the specific heat. Our result also explains how the crossover from universal to nonuniversal behaviour is realized.

Giuliani, A., Mastropietro, V. (2005). Anomalous universality in the anisotropic Ashkin-Teller model. COMMUNICATIONS IN MATHEMATICAL PHYSICS, 256(3), 681-735 [10.1007/s00220-004-1224-2].

Anomalous universality in the anisotropic Ashkin-Teller model

MASTROPIETRO, VIERI
2005-01-01

Abstract

The Ashkin-Teller (AT) model is a generalization of Ising 2-d to a four states spin model; it can be written in the form of two Ising layers (in general with different couplings) interacting via a four-spin interaction. It was conjectured long ago (by Kadanoff and Wegner, Wu and Lin, Baxter and others) that AT has in general two critical points, and that universality holds, in the sense that the critical exponents are the same as in the Ising model, except when the couplings of the two Ising layers are equal (isotropic case). We obtain an explicit expression for the specific heat from which we prove this conjecture in the weakly interacting case and we locate precisely the critical points. We find the somewhat unexpected feature that, despite universality, holds for the specific heat, nevertheless nonuniversal critical indexes appear: for instance the distance between the critical points rescale with an anomalous exponent as we let the couplings of the two Ising layers coincide (isotropic limit); and so does the constant in front of the logarithm in the specific heat. Our result also explains how the crossover from universal to nonuniversal behaviour is realized.
Pubblicato
Rilevanza internazionale
Articolo
Sì, ma tipo non specificato
Settore MAT/07 - Fisica Matematica
English
Con Impact Factor ISI
2-DIMENSIONAL ISING-MODEL; QUANTUM-FIELD-THEORY; RENORMALIZATION-GROUP; PHASE-TRANSITIONS; FERMI-SURFACE; CRITICAL EXPONENTS; 8-VERTEX MODEL; BETA-FUNCTION; ONE-DIMENSION; STATISTICS
http://www.springerlink.com/content/ct82p6jwg3na9dut/
Giuliani, A., Mastropietro, V. (2005). Anomalous universality in the anisotropic Ashkin-Teller model. COMMUNICATIONS IN MATHEMATICAL PHYSICS, 256(3), 681-735 [10.1007/s00220-004-1224-2].
Giuliani, A; Mastropietro, V
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/2108/32554
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