Stochastic resonance in the two-dimensionalq-state clock models

Abstract

We numerically study stochastic resonance in the two-dimensional q-state clock models from q = 2 to 7 under a weak oscillating magnetic field. As in the mean-field case, we observe double resonance peaks, but the detailed response strongly depends on the direction of the field modulation for q ≥ 5 where the quasiliquid phase emerges. We explain this behavior in terms of free-energy landscapes on the two-dimensional magnetization plane.

Homotopy-Theoretic Study & Atomic-Scale Observation of Vortex Domains in Hexagonal Manganites

“…In analyzing the evolution of vortex pattern, we find that the emergence of U (1) is critical for the formation of vortices, even though the final state is of Z 6 symmetry (see Movie II and III in supplementary materials ). Note also that theoretical simulations based on phase-field methods or six-state clock model can yield certain results in good agreement with our conclusion: the initial states set for Monte-Carlo calculations are disordered states that can be excited only at high temperatures, the calculation steps correspond to a quenching or annealing process accompanied by spontaneous symmetry breaking from U (1) to Z 6 , and the six-fold vortices observed in the final state are the inevitable product of this evolution process 37 38 39 40 41 .…”

Anomalous response in the vicinity of spontaneous symmetry breaking

“…The magnetization of the system is defined as a vector sum m = N −1 j s j . A weak and slow driving in-plane field h is applied in a perpendicular direction to m with amplitude h 0 ≪ 1 and angular frequency ω ≪ 1 [37]. The model in equilibrium undergoes double phase transitions, only one of which at the lower T is accompanied by spontaneous symmetry breaking.…”