Hamiltonian dynamics of the two-dimensional lattice phi^4 model

TL;DR

This paper studies the Hamiltonian dynamics of a 2D lattice phi^4 model through simulations, revealing a phase transition, critical slowing down, and links between chaos and phase behavior.

Contribution

It provides a detailed numerical analysis of the phase transition and chaos in the 2D lattice phi^4 model, connecting microscopic dynamics with macroscopic phenomena.

Findings

Identification of a continuous phase transition at finite energy density

Observation of critical slowing down near the transition

Analysis of chaos and its relation to the phase transition

Abstract

The Hamiltonian dynamics of the classical $\phi^4$ model on a two-dimensional square lattice is investigated by means of numerical simulations. The macroscopic observables are computed as time averages. The results clearly reveal the presence of the continuous phase transition at a finite energy density and are consistent both qualitatively and quantitatively with the predictions of equilibrium statistical mechanics. The Hamiltonian microscopic dynamics also exhibits critical slowing down close to the transition. Moreover, the relationship between chaos and the phase transition is considered, and interpreted in the light of a geometrization of dynamics.