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The mean-field phi4-model: entropy, analyticity, and configuration space topology

Ingo Hahn·Michael Kastner
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Abstract

A large deviation technique is applied to the mean-field phi4-model, providing an exact expression for the configurational entropy s(v,m) as a function of the potential energy v and the magnetization m. Although a continuous phase transition occurs at some critical energy v_c, the entropy is found to be a real analytic function in both arguments, and it is only the maximization over m which gives rise to a nonanalyticity in s(v)=sup_m s(v,m). This mechanism of nonanalyticity-generation by maximization over one variable of a real analytic function is restricted to systems with long-range interactions and has--for continuous phase transitions--the generic occurrence of classical critical exponents as an immediate consequence. Furthermore, this mechanism can provide an explanation why, contradictory to the so-called topological hypothesis, the phase transition in the mean-field phi4-model need not be accompanied by a topology change in the family of constant-energy submanifolds.

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Ingo Hahn, Michael Kastner. 2005-06-24. The mean-field phi4-model: entropy, analyticity, and configuration space topology. https://doi.org/10.1103/physreve.72.056134

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