# Toward a refining of the topological theory of phase transitions

5 Jun 2017Matteo GoriRoberto FranzosiMarco Pettini

The topological theory of phase transitions was proposed on the basis of different arguments, the most important of which are: a direct evidence of the relation between topology and phase transitions for some exactly solvable models; an explicit relation between entropy and topological invariants of certain submanifolds of configuration space, and, finally, two theorems stating that, for a wide class of physical systems, phase transitions should necessarily stem from topological changes of some submanifolds of configuration space. It has been recently shown that the $2D$ lattice $\phi^4$-model provides a counterexample that falsifies the mentioned theorems... (read more)

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