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On a third-order phase transition

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Abstract

The asymptotic behaviour of random variables of the general form

$$\ln \sum\limits_{i = 1}^{\kappa ^N } {\exp (N^{1/p} \beta \zeta _i )} $$

with independent identically distributed random variables ζ i is studied. This generalizes the random energy model of Derrida. In the limitN→∞, there occurs a particular kind of phase transition, which does not incorporate a bifurcation phenomenon or symmetry breaking. The hypergeometric character of the problem (see definitions of Sect. 4), its Φ-function, and its entropy function are discussed.

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Communicated by O. E. Landford

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Eisele, T. On a third-order phase transition. Commun.Math. Phys. 90, 125–159 (1983). https://doi.org/10.1007/BF01209390

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  • DOI: https://doi.org/10.1007/BF01209390

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