Hamiltonian dynamics of the two-dimensional lattice model

DOI10.1088/0305-4470/31/15/004zbMATH Open0932.82025arXivcond-mat/9804227OpenAlexW2047591624MaRDI QIDQ4254270

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Publication date: 29 June 1999

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Abstract: The Hamiltonian dynamics of the classical $ph{i}^4$ 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.

Full work available at URL: https://arxiv.org/abs/cond-mat/9804227

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