Abstract
A new analytical technique based on integral transformations with Mittag-Leffler-type kernels is used to derive the finite-size scaling function for the free energy per particle of the mean spherical model with inverse power law asymptotics of the interaction potential. The asymptotic formation of the singularities in the specific heat and magnetic susceptibility at the bulk critical point is studied.
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References
S. Singh and R. K. Pathria,Phys. Rev. B 31:4483 (1985);32:4618 (1985).
J. Shapiro and J. Rudnick,J. Stat. Phys. 43:51 (1986).
M. E. Fisher and V. Privman,Commun. Math. Phys. 103:527 (1986).
G. S. Joyce,Phys. Rev. 146:349 (1966); inPhase Transitions and Critical Phenomena, Vol. 2, C. Domb and M. S. Green, eds. (Academic Press, New York, 1972).
J. G. Brankov and N. S. Tonchev,J. Stat. Phys. 52:143 (1988).
H. Bateman and A. Erdelyi,Higher Transcedental Functions, Vol. 3 (McGraw-Hill, New York, 1955).
H. W. Lewis and G. H. Wannier,Phys. Rev. 88:682 (1952).
M. M. Djrbashyan,Integral Transformations and Representations of Functions in a Complex Domain (in Russian) (Nauka, Moscow, 1966).
P. Humbert,C. R. Acad. Sci. Paris 236:1467 (1953).
R. P. Agarwal,C. R. Acad. Sci. Paris 236:2031 (1953).
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Brankov, J.G. Finite-size scaling for the mean spherical model with inverse power law interaction. J Stat Phys 56, 309–330 (1989). https://doi.org/10.1007/BF01044439
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DOI: https://doi.org/10.1007/BF01044439