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Cambridge University Press eBooks

Mean-field theories and critical phenomena

C. Di Castro, Roberto Raimondi

Published Aug 27, 2015• 0 citations
Publisher
DOI
10.1017/cbo9781139600286.009

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Journal of the Physical Society of Japan•Jan 15, 1986•45 citations
A new method is proposed to study critical phenomena, which is a unification of Weiss' mean-field theory and Fisher's finite-size scaling theory. A systematic series of clusters is considered and generalized mean-fields are applied to the boundary spins of such clusters. From the size-dependence of the coefficients of mean-field singularities systematically obtained, the static critical exponents α, β and γ, and critical slowing down exponent Δ can be estimated. The critical point T C can be also evaluated from the size-dependence of mean-field critical points obtained in a systematic series of clusters. Some applications to the two- and three-dimensional Ising models are given explicitly to obtain T C =(2.24(0.036)) J / k B and γ=1.7(0.05) in the two-dimensional square lattice in our preliminary calculations.