Annealing Dynamics of the Two-Dimensional Fully Frustrated Ising Model
Abstract
We study the dynamical scaling properties of the two-dimensional fully frustrated Ising model by simulated annealing. The model has a highly degenerate, critical ground state with well known equilibrium properties. To study its out-of-equilibrium behavior, we develop an annealing protocol that is convenient for extending the Kibble-Zurek mechanism to the case of an exponentially divergent correlation length in the limit of the temperature T → Tc = 0. We find excellent agreement with the scaling forms derived, including a dependence on the initial temperature that is not present in the conventional Kibble-Zurek mechanism. The dynamic exponent z is consistent among all quantities studied; fits of its dependence on the initial temperature give z = 1.99(2) (susceptibility), z = 2.072(8) (excess energy), and z = 2.09(3) (Edwards-Anderson order parameter). These values are close to z=2, which is consistent with previous studies of relaxation after instantaneous quenches and of time dependent correlations in equilibrium, including the estimate z = 2.004(9) from equilibrium autocorrelation functions.
Related
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BibTeX
@misc{wu2026annealing,
title = {{Annealing Dynamics of the Two-Dimensional Fully Frustrated Ising Model}},
author = {Kai-Hsin Wu and Anders W. Sandvik and Ying-Jer Kao},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.25109},
eprint = {2610.25109},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.25109},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Annealing Dynamics of the Two-Dimensional Fully Frustrated Ising Model
AU - Kai-Hsin Wu
AU - Anders W. Sandvik
AU - Ying-Jer Kao
PY - 2026
DA - 2026/10/18
PB - arXiv
DO - 10.48550/arxiv.2610.25109
UR - https://arxiv.org/abs/2610.25109
AB - We study the dynamical scaling properties of the two-dimensional fully frustrated Ising model by simulated annealing. The model has a highly degenerate, critical ground state with well known equilibrium properties. To study its out-of-equilibrium behavior, we develop an annealing protocol that is convenient for extending the Kibble-Zurek mechanism to the case of an exponentially divergent correlation length in the limit of the temperature T → T_c = 0. We find excellent agreement with the scaling forms derived, including a dependence on the initial temperature that is not present in the conventional Kibble-Zurek mechanism. The dynamic exponent z is consistent among all quantities studied; fits of its dependence on the initial temperature give z = 1.99(2) (susceptibility), z = 2.072(8) (excess energy), and z = 2.09(3) (Edwards-Anderson order parameter). These values are close to z=2, which is consistent with previous studies of relaxation after instantaneous quenches and of time dependent correlations in equilibrium, including the estimate z = 2.004(9) from equilibrium autocorrelation functions.
ER -