Non-equilibrium dynamics of two-dimensional lattice models

A Asad, Bo-Xiao Zheng

A Asad, B Zheng

Leon J. Sieke, Mattis Harhoff, Sören Schlichting +1 more

We study the critical dynamics of a scalar field theory with Z 2 symmetry in the dynamic universality class of Model A in two and three spatial dimensions with classical-statistical lattice simulations. In particular, we measure the non-equilibrium behavior of the system under a quench protocol in which the symmetry-breaking external field is changed at a constant rate through the critical point. Using the well-established Kibble-Zurek scaling theory we compute non-equilibrium scaling functions of cumulants of the order parameter up to fourth order. Together with the static critical exponents and the dynamic critical exponent, these fully describe the universal non-equilibrium evolution of the system near the critical point. We further extend the analysis to include finite-size effects and observe good collapse of our data onto two-dimensional universal non-equilibrium and finite-size scaling functions.

Marco Schirò

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.

Minoru Takahashi, 高橋 實