Deterministic Equations of Motion and Dynamic Critical Phenomena

Abstract

Taking the two-dimensional ${\varphi }^4$ theory as an example, we numerically solve the deterministic equations of motion with random initial states. Short-time behavior of the solutions is systematically investigated. Assuming that the solutions generate a microcanonical ensemble of the system, we demonstrate that the second order phase transition point can be determined already from the short-time dynamic behavior. Initial increase of the magnetization and critical slowing down are observed. The dynamic critical exponent z, the new exponent $\theta$ and the static exponents $\beta$ and $\nu$ are estimated. Interestingly, the deterministic dynamics with random initial states is in a same dynamic universality class of Monte Carlo dynamics.

to appear in Phys. Rev. Lett

References in corpus (5)

• Generalized Dynamic Scaling for Critical Magnetic Systems
• Dynamic Approach to the Fully Frustrated XY Model
• Geometry of dynamics and phase transitions in classical lattice phi^4 theories
• Hamiltonian Dynamics and the Phase Transition of the XY Model
• Hamiltonian dynamics of the two-dimensional lattice phi^4 model

Cited by in corpus (27)

• Computer simulations of two-dimensional melting with dipole-dipole interactions
• Dynamic Approach to Weak First Order Phase Transitions
• Dynamic behavior of anisotropic non-equilibrium driving lattice gases
• Critical Behavior of an Ising System on the Sierpinski Carpet: A Short-Time Dynamics Study
• Time-reversal asymmetry in financial systems
• Aging at Criticality in Model C Dynamics
• Short-time domain-wall dynamics in the random-field Ising model with a driving field
• Monte Carlo simulations and numerical solutions of short-time critical dynamics
• Extended finite-size scaling of synchronized coupled oscillators
• Nonequilibrium critical dynamics with domain wall and surface
• Topological Effects caused by the Fractal Substrate on the Nonequilibrium Critical Behavior of the Ising Magnet
• Corrections to Scaling for the Two-dimensional Dynamic XY Model
• Monte Carlo Simulations of Short-time Critical Dynamics with a Conserved Quantity
• Dynamic effect of overhangs and islands at the depinning transition in two-dimensional magnets
• Deterministic Equations of Motion and Phase Ordering Dynamics
• Nonequilibrium critical relaxation in the presence of extended defects
• Late stages of coarsening in model C
• Short-time critical dynamics at perfect and non-perfect surface
• Short-time critical dynamics and universality on a two-dimensional Triangular Lattice
• Comment on ``Deterministic equations of motion and phase ordering dynamics''
• Short-Time Critical Dynamics of Damage Spreading in the Two-Dimensional Ising Model
• Corrections to scaling in the dynamic approach to the phase transition with quenched disorder
• Microscopic Deterministic Dynamics and Persistence Exponent
• Hamiltonian equation of motion and depinning phase transition in two-dimensional magnets
• Critical domain-wall dynamics of model B
• Dynamic relaxation of topological defect at Kosterlitz-Thouless phase transition
• Phase Ordering Dynamics of ${\varphi }^4$ Theory with Hamiltonian Equations of Motion