On the apparent failure of the topological theory of phase transitions

2016/02/03 by Gori, Matteo, Franzosi, Roberto, Pettini, Marco
#FOS: Physical sciences #Statistical Mechanics (cond-mat.stat-mech)

paper · doi:10.48550/arxiv.1602.01240

Abstract

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 ϕ⁴-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→∞) 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.

Related

• Toward a refining of the topological theory of phase transitions
• Unattainability of a Purely Topological Criterion for the Existence of a Phase Transition for Nonconfining Potentials
• Simplified energy landscape of the ϕ⁴ model and the phase transition
• Topology and Phase Transitions: Theorem on a necessary relation
• A local criterion of topological phase transitions