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First-order transitions in spherical models: Finite-size scaling

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Abstract

Finite-size behavior near the first-order phase boundary of ferromagnetic spherical models is investigated for block- and cylinder-shaped systems ind dimensions. The bulk thermodynamic singularities are rounded and, asymptotically for large size, obey appropriate scaling laws. Both short-range interactions and long-range couplings, decaying like 1/rd+σ with σ>0, are analyzed: the short-range results agree precisely with a recently developed scaling theory forO(n) symmetric systems in the limitn→∞. More generally, the scaling functions are universal, depending only on σ. Explicit aspects of the shape and interactions enter only in the “spin wave” or “Goldstone mode” contributions which appear, technically, as “corrections to scaling.” An appendix analyzes the truncation error in the approximation, by many-fold sums, of multivariate integrals with integrands diverging like [∑jajθ 2j ]-λ as θ→0.

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Author notes

  1. Michael E. Fisher

    Present address: Baker Laboratory, Cornell University, 14853, Ithaca, New York, USA

  2. Vladimir Privman

    Present address: Physics Department, Clarkson University, 13676, Potsdam, New York, USA

Authors and Affiliations

  1. Department of Theoretical Physics, University of Oxford, 1 Keble Road, OX1 3NP, Oxford, England

    Michael E. Fisher

  2. Downs Laboratory of Physics 405-47, California Institute of Technology, 91125, Pasadena, California, USA

    Vladimir Privman

Authors
  1. Michael E. Fisher
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  2. Vladimir Privman
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Communicated by A. Jaffe

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Fisher, M.E., Privman, V. First-order transitions in spherical models: Finite-size scaling. Commun.Math. Phys. 103, 527–548 (1986). https://doi.org/10.1007/BF01211164

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  • DOI: https://doi.org/10.1007/BF01211164

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