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

Abstract

In this paper we investigate the Hamiltonian dynamics of a lattice gauge model in three spatial dimension. 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 symmetry-breaking. Besides the well known use of quantities like the Wilson loop we show how else the phase transition in such a kind of models can be detected. It is found that the first order phase transition undergone by this model is characterised according to an Ehrenfest-like classification of phase transitions applied to the configurational entropy. On the basis of the topological theory of phase transitions, it is discussed why the seemingly divergent behaviour of the third derivative of configurational entropy can be considered as the "shadow" of some suitable topological transition of certain submanifolds of configuration space.

arXiv comment31 pages, 9 figures

References in corpus (26)

• Topological entanglement entropy
• Detecting topological order in a ground state wave function
• Statistical mechanics and dynamics of solvable models with long-range interactions
• Geometric approach to Hamiltonian dynamics and statistical mechanics
• Geometry of dynamics, Lyapunov exponents and phase transitions
• A Theorem on the origin of Phase Transitions
• Microcanonical entropy inflection points: Key to systematic understanding of transitions in finite systems
• Analytic estimation of Lyapunov exponent in a mean-field model undergoing a phase transition
• Phase transitions and topology changes in configuration space
• Phase transitions detached from stationary points of the energy landscape
• Geometry of dynamics and phase transitions in classical lattice phi^4 theories
• Topology and Phase Transitions II. Theorem on a necessary relation
• Topology and Phase Transitions I. Preliminary Results
• Classification of Phase Transitions by Microcanonical Inflection-Point Analysis
• Hamiltonian dynamics of the two-dimensional lattice phi^4 model
• Non-analytic microscopic phase transitions and temperature oscillations in the microcanonical ensemble: An exactly solvable 1d-model for evaporation
• Topological origin of the phase transition in a mean-field model
• Topology and phase transitions: from an exactly solvable model to a relation between topology and thermodynamics
• Phase transitions as topology changes in configuration space: an exact result
• Lyapunov exponents as a dynamical indicator of a phase transition
• Curvature fluctuations and Lyapunov exponent at Melting
• Microcanonical description of (micro) black holes
• Genuine phase diffusion of a Bose-Einstein condensate in the microcanonical ensemble: A classical field study
• Topological Approach to Microcanonical Thermodynamics and Phase Transition of Interacting Classical Spins
• Quantum field propagator for extended-objects in the microcanonical ensemble and the S-matrix formulation
• Microcanonical analysis of a nonequilibrium phase transition