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Journal of Physics C Solid State Physics

Renormalisation group recursion relations using the application of generalised Callen identities to the Ashkin-Teller model

Noureddine Benayad, A. Benyoussef, N. Boccara, Abdallah El Kenz

Published Dec 10, 1988• 36 citations
Publisher

Abstract

Using generalised Callen identities a sequence of appropriate renormalisation group recursion relations for Ising models are derived. They are simple to obtain and give very satisfactory results for critical and non-critical physical quantities. The technique is then used to derive the phase diagram and to study the critical properties of the Ashkin-Teller model.

DOI
10.1088/0022-3719/21/34/011

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Using generalised Callen identities a sequence of appropriate renormalisation group recursion relations for Ising models are derived. They are simple to obtain and give very satisfactory results for critical and non-critical physical quantities. The technique is then used to derive the phase diagram and to study the critical properties of the Ashkin-Teller model.
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.
A renormalisation group approach developed for the percolation problem by Young and Stinchcombe (1975) is extended to yield magnetic indices. A real-space cluster calculation is carried out for the Ashkin-Teller-Potts model (Ashkin & Teller 1964, Potts 1952) with general S, allowing contact with results for the Ising model (S to 2) as well as with the previously published thermal indices of the percolation problem (S to 1). For the percolation problem, the magnetic index obtained is 2.06, about 10% larger than current series estimates, and results in gamma =2.87.