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Gaussian fluctuations for the magnetization of Lee-Yang ferromagnets at zero external field

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Abstract

We consider the fluctuations of the block spin magnetization normalized by the square root of the considered number of spins in a blockΛ for Lee-Yang ferromagnets. It is established that the fluctuations are Gaussian whenΛ ↑ ℤd at zero external field whenever the susceptibility is finite (i.e., above the critical temperature) and converges to the second derivative of the pressure at zero field. The validity of this fluctuation-dissipation condition is known to hold for a large class of Lee-Yang models, including, for instance, classical Heisenberg ferromagnets.

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Author notes

  1. Joël De Coninck

    Present address: Faculté des Sciences, Université de l'Etat à Mons, 7000, Mons, Belgium

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  1. Department of Mathematics, California Institute of Technology, 91125, Pasadena, California

    Joël De Coninck

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  1. Joël De Coninck
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De Coninck, J. Gaussian fluctuations for the magnetization of Lee-Yang ferromagnets at zero external field. J Stat Phys 47, 397–407 (1987). https://doi.org/10.1007/BF01007517

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  • DOI: https://doi.org/10.1007/BF01007517

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