Abstract
A method is suggested for the derivation of finite-size corrections in the thermodynamic functions of systems with pair interaction potential decaying at large distancesr asr −d −σ, whered is the space dimensionality andσ>0. It allows for a unified treatment of short-range (σ=2) and long-range (σ<2) interaction. The asymptotic analysis is illustrated by the mean spherical model of general geometryL d−d′×∞d′ subject to periodic boundary conditions. The Fisher-Privman equation of state is generalized to arbitrary real values ofd⩾σ, 0⩽d′⩽σ. It is shown that theε-expansion may be used to study the breakdown of standard finite-size scaling at the borderline dimensionalities.
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Brankov, J.G., Tonchev, N.S. An investigation of finite-size scaling for systems with long-range interaction: The spherical model. J Stat Phys 59, 1431–1450 (1990). https://doi.org/10.1007/BF01334758
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DOI: https://doi.org/10.1007/BF01334758