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

Abstract

The Hamiltonian dynamics of the classical ${\varphi }^4$ 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.

REVTeX, 24 pages with 20 PostScript figures

References in corpus (4)

• A Dynamical Approach to Temperature
• Lyapunov instability and finite size effects in a system with long-range forces
• Geometry of dynamics, Lyapunov exponents and phase transitions
• Geometry of dynamics and phase transitions in classical lattice phi^4 theories

Cited by in corpus (29)

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• Microcanonical temperature for a classical field: application to Bose-Einstein condensation
• Topology and phase transitions: a paradigmatic evidence
• Topological aspects of geometrical signatures of phase transitions
• Weak and strong chaos in FPU models and beyond
• Topological origin of the phase transition in a mean-field model
• Non-Equilibrium Statistical Mechanics of Classical Lattice ${\varphi }^4$ Field Theory
• Aging at Criticality in Model C Dynamics
• Hamiltonian dynamics and geometry of phase transitions in classical XY models
• Non-Equilibrium Steady States and Transport in the Classical Lattice ${\varphi }^4$ Theory
• Chaotic properties of spin lattices near second-order phase transitions
• Deterministic Equations of Motion and Phase Ordering Dynamics
• Topological Theory of Phase Transitions
• Late stages of coarsening in model C
• On the clustering phase transition in self-gravitating N-body systems
• Relaxation of 2+1 dimensional classical O(2) symmetric scalar fields
• The Geometric Theory of Phase Transitions
• Dynamical approach to the microcanonical ensemble
• Comment on ``Deterministic equations of motion and phase ordering dynamics''
• Coarsening of two dimensional XY model with Hamiltonian dynamics: Logarithmically divergent vortex mobility
• Hydrodynamics and transport in the long-range-interacting ${\phi }^4$ chain
• Efficient time series detection of the strong stochasticity threshold in Fermi-Pasta-Ulam oscillator lattices
• Geometric approach to chaos in the classical dynamics of abelian lattice gauge theory
• Hamiltonian equation of motion and depinning phase transition in two-dimensional magnets
• Many-body chaos and anomalous diffusion across thermal phase transitions in two dimensions
• On the origin of Phase Transitions in the absence of Symmetry-Breaking