Matching procedures, related to the group structure of block-spin renormalization, are proposed for an optimal choice of parameter-dependent transformations. The method also allows to determine the parameter's dependence on the reduced coupling near the fixed point. Applications to linear transformations for two- and three-dimensional Ising models and two-dimensional three-, four-, and five-state Potts systems are reported. With simple approximations good estimates of critical couplings and exponents are obtained. Results for the two-dimensional spin-1/2 XY system and their possible implications, as far as an eventual transition is concerned, are discussed. Some applications to nonlinear transformations are also considered
GROUP-STRUCTURE OF BLOCK TRANSFORMATIONS - MATCHING CONDITIONS FOR THE CRITICAL PROPERTIES OF LATTICE SPIN SYSTEMS
STELLA, ATTILIO;TOIGO, FLAVIO
1979
Abstract
Matching procedures, related to the group structure of block-spin renormalization, are proposed for an optimal choice of parameter-dependent transformations. The method also allows to determine the parameter's dependence on the reduced coupling near the fixed point. Applications to linear transformations for two- and three-dimensional Ising models and two-dimensional three-, four-, and five-state Potts systems are reported. With simple approximations good estimates of critical couplings and exponents are obtained. Results for the two-dimensional spin-1/2 XY system and their possible implications, as far as an eventual transition is concerned, are discussed. Some applications to nonlinear transformations are also consideredPubblicazioni consigliate
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