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 Conference Series

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

Ivan S Popov, Anna P Popova, Pavel Vladimirovich Prudnikov

Published Feb 1, 2019• 0 citations
Publisher

Abstract

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.

DOI
10.1088/1742-6596/1163/1/012039

Related papers

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

Quench dynamics of the 2dXYmodel

Asja Jelić, Leticia F. Cugliandolo

We investigate the out of equilibrium dynamics of the two-dimensional XY model when cooled across the Berezinskii–Kosterlitz–Thouless (BKT) phase transition using different protocols. We focus on the evolution of the growing correlation length and the density of topological defects (vortices). By using Monte Carlo simulations we first determine the time and temperature dependence of the growing correlation length after an infinitely rapid quench from above the transition temperature to the quasi-long-range order region. The functional form is consistent with a logarithmic correction to the diffusive law and it serves to validate dynamic scaling in this problem. This analysis clarifies the different dynamic roles played by bound and free vortices. We then revisit the Kibble–Zurek mechanism in thermal phase transitions in which the disordered state is plagued with topological defects. We provide a theory of quenching rate dependence in systems with the BKT-type transition that goes beyond the equilibrium scaling arguments. Finally, we discuss the implications of our results for a host of physical systems with vortex excitations, including planar ferromagnets and liquid crystals.

arXiv:1012.0417•Journal of Statistical Mechanics Theory and Experiment•Feb 18, 2011•89 citations

Semi-vortices and cluster-vorticity: new concepts in the Berezinskii-Kosterlitz-Thouless phase transition

Brandon Gómez Bravo, Bryan David Juárez Hernández, Wolfgang Bietenholz A

The Berezinski˘ı-Kosterlitz-Thouless (BKT) essential phase transition in the 2d XY model is revisited. Its mechanism is usually described by the (un)binding of vortex–anti-vortex (V–AV) pairs, which does, however, not provide a clear-cut quantitative criterion for criticality. Known sharp criteria are the divergence of the correlation length and a discontinuity of the helicity modulus. Here we propose and probe a new criterion: it is based on the concepts of semi-vortices and cluster vorticity, which are formulated in the framework of the multi-cluster algorithm that we use to simulate the 2d XY model

arXiv:2206.01854•Suplemento de la Revista Mexicana de Física•Jun 25, 2022•3 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

Short-time critical dynamics and aging phenomena in the two-dimensional XY model

X. W. Lei, Bo Zheng

With Monte Carlo methods, we simulate dynamic relaxation processes of the two-dimensional XY model at the Berezinskii-Kosterlitz-Thouless phase transition temperature and below, starting from both ordered and disordered initial states. The two-time correlation function A(t',t) is measured, and aging phenomena are investigated. The power-law correction in the spatial correlation length xi(t) for relaxation with an ordered initial state and the logarithmic correction for relaxation with a disordered initial state are carefully analyzed. The scaling functions of A(t',t) are then extracted.

Physical Review E•Apr 12, 2007•33 citations

Dynamical Scaling in Time dependence of Correlation Length in Non-equilibrium Critical Relaxation of Pure and Site-diluted 2D XY-model

Ivan S Popov, Anna P Popova, Pavel Vladimirovich Prudnikov +1 more

Structural disorder in two-dimensional XY-model creates an anomalous slowing down in the process of critical relaxation. Dynamic dependences of the correlation length ξ ( t ) show slow growth with an "effective" dynamical critical exponent z > 2. For a pure system, it has been shown that a detailed consideration of the vortex dynamics leads to deviations from the known dependence ξ ( t ) ∼ ( t /ln t ) 1/2 .

Journal of Physics Conference Series•Feb 1, 2019•0 citations
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).
We investigate the out of equilibrium dynamics of the two-dimensional XY model when cooled across the Berezinskii–Kosterlitz–Thouless (BKT) phase transition using different protocols. We focus on the evolution of the growing correlation length and the density of topological defects (vortices). By using Monte Carlo simulations we first determine the time and temperature dependence of the growing correlation length after an infinitely rapid quench from above the transition temperature to the quasi-long-range order region. The functional form is consistent with a logarithmic correction to the diffusive law and it serves to validate dynamic scaling in this problem. This analysis clarifies the different dynamic roles played by bound and free vortices. We then revisit the Kibble–Zurek mechanism in thermal phase transitions in which the disordered state is plagued with topological defects. We provide a theory of quenching rate dependence in systems with the BKT-type transition that goes beyond the equilibrium scaling arguments. Finally, we discuss the implications of our results for a host of physical systems with vortex excitations, including planar ferromagnets and liquid crystals.
The Berezinski˘ı-Kosterlitz-Thouless (BKT) essential phase transition in the 2d XY model is revisited. Its mechanism is usually described by the (un)binding of vortex–anti-vortex (V–AV) pairs, which does, however, not provide a clear-cut quantitative criterion for criticality. Known sharp criteria are the divergence of the correlation length and a discontinuity of the helicity modulus. Here we propose and probe a new criterion: it is based on the concepts of semi-vortices and cluster vorticity, which are formulated in the framework of the multi-cluster algorithm that we use to simulate the 2d XY model
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.
With Monte Carlo methods, we simulate dynamic relaxation processes of the two-dimensional XY model at the Berezinskii-Kosterlitz-Thouless phase transition temperature and below, starting from both ordered and disordered initial states. The two-time correlation function A(t',t) is measured, and aging phenomena are investigated. The power-law correction in the spatial correlation length xi(t) for relaxation with an ordered initial state and the logarithmic correction for relaxation with a disordered initial state are carefully analyzed. The scaling functions of A(t',t) are then extracted.