New Method to Study Critical Phenomena-Mean-Field Finite-Size Scaling Theory

概要

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A new method is proposed to study critical plaenomena, which is a unification ofWeiss' mean-field theory and Fisher's finite-size scaling theory. A systematic series ofclusters is considered and generalized mean-fields are applied to the boundary spinsof such clusters.From the size-dependence of the coefficients of mean-field singularitiessystematically obtained, the static critical exponents a, 73 and y, and critical slowingdown exponent A can be estimated. The critical point T. COIN be also evaluated fromthe size-dependence of mean-field critical points obtained in a systematic series ofclusters. Some applications to the two- and three?-dimensional Ising models are givenexplicitly to obtain T.,=(2.24(0.036))J/k. and 7=1.7(0.05) in the two-dimensionalsquare lattice in our prelimimaary calculations.
社団法人日本物理学会の論文
1986-01-15