Mean-field expansion for spin models with medium-range interactions

Abstract

We study the critical crossover between the Gaussian and the Wilson-Fisher fixed point for general O(N)-invariant spin models with medium-range interactions. We perform a systematic expansion around the mean-field solution, obtaining the universal crossover curves and their leading corrections. In particular we show that, in three dimensions, the leading correction scales as $R^{-3},R$ being the range of the interactions. We compare our results with the existing numerical ones obtained by Monte Carlo simulations and present a critical discussion of other approaches.

49 pages, 8 figures

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• Classical-to-critical crossovers from field theory
• Crossover behavior in three-dimensional dilute spin systems
• Crossover behavior in He3 and Xe near their liquid-vapor critical point
• Critical mass renormalization in renormalized phi4 theories in two and three dimensions
• Two-Dimensional Heisenberg Model with Nonlinear Interactions: 1/N Corrections
• Crossover phenomena in spin models with medium-range interactions and self-avoiding walks with medium-range jumps
• Violation of the Widom scaling law for effective crossover exponents
• Generalized Crossover in multiparameter Hamiltonians
• Large-N_f chiral transition in the Yukawa model