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Pré-Publication, Document De Travail Année : 2015

On the apparent failure of the topological theory of phase transitions

Résumé

The topological theory of phase transitions has its strong point in two theorems proving that, for a wide class of physical systems, phase transitions necessarily stem from topological changes of some submanifolds of configuration space. It has been recently argued that the $2D$ lattice $\phi^4$-model provides a counterexample that falsifies this theory. It is here shown that this is not the case: the phase transition of this model stems from an asymptotic ($N\to\infty$) change of topology of the energy level sets, in spite of the absence of critical points of the potential in correspondence of the transition energy.

Dates et versions

hal-01273815 , version 1 (14-02-2016)

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Matteo Gori, Roberto Franzosi, Marco Pettini. On the apparent failure of the topological theory of phase transitions. 2015. ⟨hal-01273815⟩
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