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 thermodynamic 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 is the effect of a deeper geometrical transition of the equipotential submanifolds of configuration space, which, in its turn, is likely to be the "shadow" of an even deeper transition of topological kind.
On the origin of phase transitions in the absence of symmetry-breaking / Giulio Pettini, Matteo Gori, Roberto Franzosi, Cecilia Clementi, Marco Pettini. - In: PHYSICA. A. - ISSN 0378-4371. - STAMPA. - 516:(2019), pp. 376-392. [10.1016/j.physa.2018.10.001]
On the origin of phase transitions in the absence of symmetry-breaking
Giulio PettiniMembro del Collaboration Group
;Roberto Franzosi
Membro del Collaboration Group
;
2019
Abstract
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 thermodynamic 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 is the effect of a deeper geometrical transition of the equipotential submanifolds of configuration space, which, in its turn, is likely to be the "shadow" of an even deeper transition of topological kind.File | Dimensione | Formato | |
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