Ornstein-zernike Theory for the Finite Range Ising
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Rigorous nonperturbative Ornstein-Zernike theory for Ising ferromagnets
– We rigorously derive the Ornstein-Zernike asymptotics of the pair-correlation functions for finite-range Ising ferromagnets in any dimensions and at any temperature above critical. The celebrated heuristic argument by Ornstein and Zernike [1] implies that the asymptotic form of the truncated two-point density correlation function of simple fluids away from the critical region is given by G(~r...
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We derive precise Ornstein-Zernike asymptotic formula for the decay of the two-point function 〈σ0σx〉β in the general context of finite range Ising type models on Z . The proof relies in an essential way on the a-priori knowledge of the strict exponential decay of the two-point function and, by the sharp characterization of phase transition due to Aizenman, Barsky and Fernández, goes through in ...
متن کاملORNSTEIN-ZERNIKE THEORY FOR FINITE RANGE ISING MODELS ABOVE Tc
We derive a precise Ornstein-Zernike asymptotic formula for the decay of the two-point function 〈σ0σx〉β in the general context of finite range Ising type models on Z. The proof relies in an essential way on the a-priori knowledge of the strict exponential decay of the two-point function and, by the sharp characterization of phase transition due to Aizenman, Barsky and Fernández, goes through in...
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The name Ising has come to stand not only for a specific model, but for an entire universality class arguably the most important such class in the theory of critical phenomena. I review several examples, both in and out of equilibrium, in which Ising universality appears or is pertinent. The “Ornstein-Zernike” connection concerns a thermodynamically self-consistent closure of the eponymous rela...
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