On the apparent failure of the topological theory of phase transitions

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 ${\varphi }^4$-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.

5 pages, 4 figures

References in corpus (1)

• Phase transitions detached from stationary points of the energy landscape

Cited by in corpus (3)

• Topological Approach to Microcanonical Thermodynamics and Phase Transition of Interacting Classical Spins
• Topology of configuration space of the mean-field phi^4 model by Morse theory
• Necessary and sufficient conditions for ${\mathbb{Z}}_2$-symmetry-breaking phase transitions