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Physica A Statistical Mechanics and its Applications

An improved theory of higher-order correlations for an Ising model with general spin

Ladislav Šamaj

Published Dec 1, 1988• 2 citations
Publisher
DOI
10.1016/0378-4371(88)90239-7

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An analytic method for finding the highly accurate values of the critical point for cubic Ising models with arbitrary spin is presented. The thermodynamic quantities of interest are expressed through some higher-order correlations with a reference spin excluded. A reduction scheme for these higher-order correlations is constructed. It leads to two types of resulting equations for correlation functions. The coincidence of two different representations of critical correlations is ensured by the introduced parameter of the reduction scheme. The estimation of critical points for all cubic lattices is compatible with series works to within 1.69%, 0.70% for the limiting values of spin, ½ and ∞, respectively.
Using conformal field theory techniques, we compute the disorder-averaged p -th power of the spin-spin correlation function (overline⟨σ(0)σ( R )⟩ p , p ∊ Z ) for the ferromagnetic random bond Potts model. We thus generalize the calculations of Dotsenko, Dotsenko and Picco ( hep-th/9709136 , 1997), where the case p = 2 was considered, and of Ludwig ( Nucl. Phys. B , 85 (1987) 97, 330 (1990) 639), where first-order computations where made for general p . Perturbative calculations are made up to second order in ( being proportional to the central charge deviation of the pure model from the Ising model value). The explicit dependence of the correlation function on p gives an upper bound for the validity of the -expansion, which seems to be valid, in the three-states case, only if p ⩽ 4.