Topological origin of phase transitions in the absence of critical points of the energy landscape
Matteo Gori, Roberto Franzosi, Marco Pettini · Journal of Statistical Mechanics Theory and Experiment · 2018
Abstract Different arguments led us to surmise that the deep origin of phase transitions has to be identified with suitable topological changes of potential-related submanifolds of configuration space of a physical system. An important step forward for this approach was achieved with two theorems stating that, for a wide class of physical systems, phase transitions should necessarily stem from topological changes of equipotential energy submanifolds of configuration space. However, it has been recently shown that the 2 D lattice -model provides a counterexample that falsifies the mentioned theorems. On the basis of a numerical investigation, the present work indicates the way to overcome this difficulty: in spite of the absence of critical points of the potential in correspondence of the transition energy, also the phase transition of this model stems from a change of topology of both the energy and potential level sets. But in this case the topology changes are asymptotic ( ). This fact is not obvious since the symmetry-breaking transition could be given measure-based explanations in presence of trivial topology.