Exact differential real-space renormalization: Ising, Gaussian and Ashkin-Teller models

H.J. Hilhorst and J.M.J.Van Leeuwen

Physica A: Statistical Mechanics and its Applications, 1981, vol. 106, issue 1, 301-310

Abstract: Two triangular Ising models are coupled by a small four-spin interaction of a generalized Ashkin-Teller type. All interactions are spatially dependent. To lowest order in perturbation theory a closed system of exact real-space renormalization equations is derived. From this system a set of nine partial differential equations decouples which describes the renormalization of nine “collective” variables: three pair interactions and six four-spin interactions. The study of these equations has revealed a marginal direction, which we interpret as a line of fixed points. Its relation to Baxter's line is discussed. Our study of the Ashkin-Teller model is preceded by a coherent presentation of the differential renormalization equations for the Ising and Gaussian model.

Date: 1981
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Persistent link: https://EconPapers.repec.org/RePEc:eee:phsmap:v:106:y:1981:i:1:p:301-310

DOI: 10.1016/0378-4371(81)90228-4

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