On the origin of Phase Transitions in the absence of Symmetry-Breaking

Giulio Pettini , Matteo Gori (1, 2) , Roberto Franzosi (3) , Cecilia Clementi , Marco Pettini (1, 2)

1 CPT - Centre de Physique Théorique - UMR 7332
2 CPT - E7 Systèmes dynamiques : théories et applications
3 C.N.I.S.M. UdR di Firenze and Dipartimento di Fisica

In this paper we investigate the Hamiltonian dynamics of a lattice gauge model in three spatial dimensions. Our model Hamiltonian is defined on the basis of a continuum version of a duality transformation of a three dimensional Ising model. The system so obtained undergoes a thermo-dynamic phase transition in the absence of a global symmetry-breaking and thus in the absence of an order parameter. It is found that the first order phase transition undergone by this model fits into a microcanonical version of an Ehrenfest-like classification of phase transitions applied to the configurational entropy. It is discussed why the seemingly divergent behaviour of the third derivative of configurational entropy can be considered as the " shadow " of some suitable geometrical and topological transition of the equipotential submanifolds of configuration space.

Domaines: Mécanique statistique [cond-mat.stat-mech]

Giulio Pettini, Matteo Gori, Roberto Franzosi, Cecilia Clementi, Marco Pettini. On the origin of Phase Transitions in the absence of Symmetry-Breaking. Physica A: Statistical Mechanics and its Applications, 2019, 516, pp.376-392. ⟨10.1016/j.physa.2018.10.001⟩. ⟨hal-01776292⟩