Finite size scaling RG: detailed description and applications to diluted Ising systems

João Monteiro de Figueiredo Neto, Suzana Maria Moss de Oliveira and Paulo Murilo Castro de Oliveira

Physica A: Statistical Mechanics and its Applications, 1994, vol. 206, issue 3, 463-478

Abstract: The finite size scaling renormalisation group (FSSRG) was introduced in Europhysics Letters 20 (1992) 621. Based only on the finite size scaling hypothesis, with no further assumptions, it differs from other real space renormalisation groups (RSRGs) in the following essential point: one does not need to adopt any particular recipe exp(-H′(S′/T = σsP(S, S′) exp[-H(S)/T] relating the spin states S of the original system to the spin states S' of a renormalised system. The choice of a particular weight function P(S, S′), e.g. the so called majority rule, is generally based on plausibility arguments, and involves uncontrollable approximations. In addition to being free from these drawbacks, FSSRG shares with RSRG some good features as, for instance, the possibility of extracting qualitative informations from multi-parameter RG flow diagrams, including crossovers, universality classes, universality breakings, multicriticalities, orders of transitions, etc. Other unpleasant consequences of particular weight functions, as the so called proliferation of parameters, are also absent in the FSSRG. Using it in three-dimensions, we were able to find a semi-unstable fixed point in the critical frontier concentration p versus exchange coupling J, characterizing a universality class crossover when one goes from pure to diluted Ising ferromagnets. The specific heat exponents we have obtained for the pure and diluted regimes are in agreement with the Harris criterion.

Date: 1994
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Persistent link: https://EconPapers.repec.org/RePEc:eee:phsmap:v:206:y:1994:i:3:p:463-478

DOI: 10.1016/0378-4371(94)90318-2

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