Topological origin of phase transitions in the absence of critical points of the energy landscape

Abstract : Different arguments led 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 2D lattice φ 4-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 (N → ∞). This fact is not obvious since the Z 2 symmetry-breaking transition could be given measure-based explanations in presence of trivial topology. * Electronic address:
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Matteo Gori, Roberto Franzosi, Marco Pettini. Topological origin of phase transitions in the absence of critical points of the energy landscape. Journal of Statistical Mechanics: Theory and Experiment, IOP Publishing, 2018, 2018, pp.093204. ⟨10.1088/1742-5468/aad6b6⟩. ⟨hal-01776027⟩

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