Dual time scales in simulated annealing of a two-dimensional Ising spin glass
Rubin, Shanon J.
Sandvik, Anders W.
MetadataShow full item record
Citation (published version)Shanon J Rubin, Na Xu, Anders W Sandvik. 2017. "Dual time scales in simulated annealing of a two-dimensional Ising spin glass." Physical Review E, Volume 95, Issue 5, 052133. https://doi.org/10.1103/PhysRevE.95.052133
We apply a generalized Kibble-Zurek out-of-equilibrium scaling ansatz to simulated annealing when approaching the spin-glass transition at temperature T=0 of the two-dimensional Ising model with random J=±1 couplings. Analyzing the spin-glass order parameter and the excess energy as functions of the system size and the annealing velocity in Monte Carlo simulations with Metropolis dynamics, we find scaling where the energy relaxes slower than the spin-glass order parameter, i.e., there are two different dynamic exponents. The values of the exponents relating the relaxation time scales to the system length, τ∼Lz, are z=8.28±0.03 for the relaxation of the order parameter and z=10.31±0.04 for the energy relaxation. We argue that the behavior with dual time scales arises as a consequence of the entropy-driven ordering mechanism within droplet theory. We point out that the dynamic exponents found here for T→0 simulated annealing are different from the temperature-dependent equilibrium dynamic exponent zeq(T), for which previous studies have found a divergent behavior: zeq(T→0)→∞. Thus, our study shows that, within Metropolis dynamics, it is easier to relax the system to one of its degenerate ground states than to migrate at low temperatures between regions of the configuration space surrounding different ground states. In a more general context of optimization, our study provides an example of robust dense-region solutions for which the excess energy (the conventional cost function) may not be the best measure of success.
Showing items related by title, author, creator and subject.
Citro, Roberta; Dalla Torre, Emanuele G.; D'Alessio, Luca; Polkovnikov, Anatoli; Babadi, Mehrtash; Oka, Takashi; Demler, Eugene (ACADEMIC PRESS INC ELSEVIER SCIENCE, 2015-09-01)We consider a many-body generalization of the Kapitza pendulum: the periodically-driven sine–Gordon model. We show that this interacting system is dynamically stable to periodic drives with finite frequency and amplitude. ...
Davidson, Shainen M.; Sels, Dries; Polkovnikov, Anatoli (ACADEMIC PRESS INC ELSEVIER SCIENCE, 2017-09-01)Understanding the behaviour of interacting fermions is of fundamental interest in many fields ranging from condensed matter to high energy physics. Developing numerically efficient and accurate simulation methods is an ...
Generation of electric fields and currents by neutral flows in weakly ionized plasmas through collisional dynamos Dimant, Y.S.; Oppenheim, M.M.; Fletcher, A.C. (AMER INST PHYSICS, 2016-08-01)In weakly ionized plasmas neutral flows drag plasma across magnetic field lines generating intense electric fields and currents. An example occurs in the Earth's ionosphere near the geomagnetic equator. Similar processes ...