Microscopic Deterministic Dynamics and Persistence Exponent

Numerically we solve the microscopic deterministic equations of motion with random initial states for the two-dimensional $\phi^4$ theory. Scaling behavior of the persistence probability at criticality is systematically investigated and the persistence exponent is estimated.Comment: to appear in Mod. Phys. Lett.

Phase Ordering Dynamics of ϕ4\phi^4 Theory with Hamiltonian Equations of Motion

Phase ordering dynamics of the (2+1)- and (3+1)-dimensional $\phi^4$ theory with Hamiltonian equations of motion is investigated numerically. Dynamic scaling is confirmed. The dynamic exponent $z$ is different from that of the Ising model with dynamics of model A, while the exponent $\lambda$ is the same.Comment: to appear in Int. J. Mod. Phys.

Topological origin of the phase transition in a mean-field model

We argue that the phase transition in the mean-field XY model is related to a particular change in the topology of its configuration space. The nature of this topological transition can be discussed on the basis of elementary Morse theory using the potential energy per particle V as a Morse function. The value of V where such a topological transition occurs equals the thermodynamic value of V at the phase transition and the number of (Morse) critical points grows very fast with the number of particles N. Furthermore, as in statistical mechanics, also in topology the way the thermodynamic limit is taken is crucial.Comment: REVTeX, 5 pages, with 1 eps figure included. Some changes in the text. To appear in Physical Review Letter

Topological aspects of geometrical signatures of phase transitions

Certain geometric properties of submanifolds of configuration space are numerically investigated for classical lattice phi^4 models in one and two dimensions. Peculiar behaviors of the computed geometric quantities are found only in the two-dimensional case, when a phase transition is present. The observed phenomenology strongly supports, though in an indirect way, a recently proposed topological conjecture about a topology change of the configuration space submanifolds as counterpart of a phase transition.Comment: REVTEX file, 4 pages, 5 figure

Comment on ``Deterministic equations of motion and phase ordering dynamics''

Zheng [Phys. Rev. E {\bf 61}, 153 (2000), cond-mat/9909324] claims that phase ordering dynamics in the microcanonical $\phi^4$ model displays unusual scaling laws. We show here, performing more careful numerical investigations, that Zheng only observed transient dynamics mostly due to the corrections to scaling introduced by lattice effects, and that Ising-like (model A) phase ordering actually takes place at late times. Moreover, we argue that energy conservation manifests itself in different corrections to scaling.Comment: 5 pages, 4 figure

Hamiltonian equation of motion and depinning phase transition in two-dimensional magnets

Based on the Hamiltonian equation of motion of the $\phi^4$ theory with quenched disorder, we investigate the depinning phase transition of the domain-wall motion in two-dimensional magnets. With the short-time dynamic approach, we numerically determine the transition field, and the static and dynamic critical exponents. The results show that the fundamental Hamiltonian equation of motion belongs to a universality class very different from those effective equations of motion.Comment: 6 pages, 7 figures, have been accept by EP

Phase transitions as topology changes in configuration space: an exact result

The phase transition in the mean-field XY model is shown analytically to be related to a topological change in its configuration space. Such a topology change is completely described by means of Morse theory allowing a computation of the Euler characteristic--of suitable submanifolds of configuration space--which shows a sharp discontinuity at the phase transition point, also at finite N. The present analytic result provides, with previous work, a new key to a possible connection of topological changes in configuration space as the origin of phase transitions in a variety of systems.Comment: REVTeX file, 5 pages, 1 PostScript figur

Geometric approach to chaos in the classical dynamics of abelian lattice gauge theory

A Riemannian geometrization of dynamics is used to study chaoticity in the classical Hamiltonian dynamics of a U(1) lattice gauge theory. This approach allows one to obtain analytical estimates of the largest Lyapunov exponent in terms of time averages of geometric quantities. These estimates are compared with the results of numerical simulations, and turn out to be very close to the values extrapolated for very large lattice sizes even when the geometric quantities are computed using small lattices. The scaling of the Lyapunov exponent with the energy density is found to be well described by a quadratic power law.Comment: REVTeX, 9 pages, 4 PostScript figures include

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

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.Comment: REVTeX, 24 pages with 20 PostScript figure

Aging at Criticality in Model C Dynamics

We study the off-equilibrium two-point critical response and correlation functions for the relaxational dynamics with a coupling to a conserved density (Model C) of the O(N) vector model. They are determined in an \epsilon=4-d expansion for vanishing momentum. We briefly discuss their scaling behaviors and the associated scaling forms are determined up to first order in epsilon. The corresponding fluctuation-dissipation ratio has a non trivial large time limit in the aging regime and, up to one-loop order, it is the same as that of the Model A for the physically relevant case N=1. The comparison with predictions of local scale invariance is also discussed.Comment: 13 pages, 1 figur