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

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

1998-04-21

arxiv.org/abs/cond-mat/9804227v1

J.Phys.A31:3357-3382,1998

Physics

Condensed Matter

Statistical Mechanics

REVTeX, 24 pages with 20 PostScript figures

Scientific paper

10.1088/0305-4470/31/15/004

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.

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