Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

Journal of Physics A Mathematical and Theoretical

Non-equilibrium critical dynamics of two-dimensional XY model with Hamiltonian equations of motion

A Asad, Bo-Xiao Zheng

Published Oct 7, 2008• 0 citations
Publisher
DOI
10.1088/1751-8121/41/44/449801

Related papers

Non-equilibrium critical dynamics of two-dimensional XY model with Hamiltonian equations of motion

A Asad, B Zheng

Journal of Physics A Mathematical and Theoretical•Oct 7, 2008•0 citations

Critical dynamics in the two-dimensional XY-model

David Paul Landau, R.W. Gerling

Journal of Magnetism and Magnetic Materials•Feb 1, 1992•15 citations

Non-equilibrium critical dynamics of the two-dimensional XY model with Hamiltonian equations of motion

A Asad, Bo Zheng

Non-equilibrium critical dynamics of the two-dimensional XY model is investigated with Hamiltonian equations of motion. Critical relaxation starting from both ordered and random states is carefully analyzed, and the short- time dynamic scaling behavior is revealed. Logarithmic corrections to scaling are detected for relaxation with a random initial state, while power-law corrections to scaling are observed for relaxation with an ordered initial state. The static exponent η and dynamic exponent z are determined around and below the Kosterlitz-Thouless phase transition temperature. Our results show that the deterministic dynamics described by Hamiltonian equations is in the same universality class as the stochastic dynamics described by Monte Carlo algorithms and Langevin equations.

Journal of Physics A Mathematical and Theoretical•Aug 1, 2007•9 citations

Critical dynamics of the four-dimensional XY model

Lars Melwyn Jensen

Physica B Condensed Matter•Jul 1, 2000•5 citations

Disorder Aggregation by Vortices in Non-Equilibrium Critical Annealing of Two-Dimensional XY-model

Ivan S Popov, Anna P Popova, Pavel Vladimirovich Prudnikov

It is shown that the non-equilibrium vortex annealing of structural disorder in a two-dimensional XY-model leads to a non-equilibrium critical coarsening. Large clusters are separated into an individual subsystem, the relaxation dynamics of which is much slower than the relaxation dynamics of the cluster subsystem as a whole. Despite the fact that the main equilibrium critical properties, even the Berezinskii-Kosterlitz-Thouless phase transition temperature T BKT ( p ), of the two-dimensional XY-model with disorder thermalization do not change as compared with the system with quench disorder, the non-equilibrium critical relaxation shows significant differences.

Journal of Physics Conference Series•Feb 1, 2019•0 citations

Non-equilibrium vortex annealing of structural disorder in the critical relaxation of diluted two-dimensional XY-model

Ivan S Popov, Anna P Popova, Pavel Vladimirovich Prudnikov

Abstract The study of the effects of aging in the non-equilibrium critical relaxation of a two-dimensional XY-model with a non-equilibrium vortex annealing of structural disorder has been carried out. Two-time dynamic dependencies of the spin-spin and defect-defect autocorrelation functions C SS (t,t w) and C DD (t,t w) are obtained for the entire Berezinskii low-temperature phase T < T BKT(p), for a wide range of waiting times t w and spin concentrations p. Near the BKT phase transition point T BKT (p), the dynamic dependencies C DD(t,t w) become uniform with time. However, with a decrease in temperature in the low-temperature phase T < T BKT (p), this relaxation uniformity breaks down, and C DD(t,t w) does not exhibit canonical aging properties. The formation of a declining family of dynamical scaling curves is clearly observed at large observation times t – t w which may indicate the presence of an asymptotic scaling dependence of C DD (t, t w).

Journal of Physics Conference Series•Nov 1, 2019•0 citations
Non-equilibrium critical dynamics of the two-dimensional XY model is investigated with Hamiltonian equations of motion. Critical relaxation starting from both ordered and random states is carefully analyzed, and the short- time dynamic scaling behavior is revealed. Logarithmic corrections to scaling are detected for relaxation with a random initial state, while power-law corrections to scaling are observed for relaxation with an ordered initial state. The static exponent η and dynamic exponent z are determined around and below the Kosterlitz-Thouless phase transition temperature. Our results show that the deterministic dynamics described by Hamiltonian equations is in the same universality class as the stochastic dynamics described by Monte Carlo algorithms and Langevin equations.
It is shown that the non-equilibrium vortex annealing of structural disorder in a two-dimensional XY-model leads to a non-equilibrium critical coarsening. Large clusters are separated into an individual subsystem, the relaxation dynamics of which is much slower than the relaxation dynamics of the cluster subsystem as a whole. Despite the fact that the main equilibrium critical properties, even the Berezinskii-Kosterlitz-Thouless phase transition temperature T BKT ( p ), of the two-dimensional XY-model with disorder thermalization do not change as compared with the system with quench disorder, the non-equilibrium critical relaxation shows significant differences.
Abstract The study of the effects of aging in the non-equilibrium critical relaxation of a two-dimensional XY-model with a non-equilibrium vortex annealing of structural disorder has been carried out. Two-time dynamic dependencies of the spin-spin and defect-defect autocorrelation functions C SS (t,t w) and C DD (t,t w) are obtained for the entire Berezinskii low-temperature phase T < T BKT(p), for a wide range of waiting times t w and spin concentrations p. Near the BKT phase transition point T BKT (p), the dynamic dependencies C DD(t,t w) become uniform with time. However, with a decrease in temperature in the low-temperature phase T < T BKT (p), this relaxation uniformity breaks down, and C DD(t,t w) does not exhibit canonical aging properties. The formation of a declining family of dynamical scaling curves is clearly observed at large observation times t – t w which may indicate the presence of an asymptotic scaling dependence of C DD (t, t w).