FINITE-SIZE-SCALING RG - DETAILED DESCRIPTION AND APPLICATIONS TO DILUTED ISING SYSTEMS

The finite size scaling renormalisation group (FSSRG) was introduced i n Europhysics Letters 20 (1992) 621. Based only on the finite size sca ling hypothesis, with no further assumptions, it differs from other re al space renormalisation groups (RSRGs) in the following essential poi nt: one does not need to adopt any particular recipe exp(-H(S')/T = SI GMA(s) P(S, S') exp[-H(S)/T] relating the spin states S of the origina l 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 ru le, is generally based on plausibility arguments, and involves uncontr ollable approximations. In addition to being free from these drawbacks , FSSRG shares with RSRG some good features as, for instance, the poss ibility of extracting qualitative informations from multi-parameter RG flow diagrams, including crossovers, universality classes, universali ty breakings, multicriticalities, orders of transitions, etc. Other un pleasant consequences of particular weight functions, as the so called proliferation of parameters, are also absent in the FSSRG. Using it i n three-dimensions, we were able to find a semi-unstable fixed point i n the critical frontier concentration p versus exchange coupling J, ch aracterizing a universality class crossover when one goes from pure to diluted Ising ferromagnets. The specific heat exponents we have obtai ned for the pure and diluted regimes are in agreement with the Harris criterion.