The phenomenon of resonance in the continuous phase transition of finite-size systems: A passage from Classical World to Quantum World through the resonance?

Abstract

In finite-size systems undergoing a continuous phase transition, the passage from the symmetric phase to the broken-symmetry phase is accomplished through a hysteresis zone, up to spontaneous symmetry breaking (SSB). In the present work, we find that a resonance phenomenon takes place within this zone. This resonance is manifested as a maximization of the mean waiting time as a function of temperature inside the hysteresis region. An interesting issue concerns how this resonance is connected with the existence of particles (tachyons) or quasiparticles (kink solitons) within the hysteresis zone. Finally, we introduce the idea that this resonance delineates a continuous passage from a "classical" phase to a "quantum" phase for a binary system, such as the three-dimensional Ising model, which belongs to the same universality class as a fermion-antifermion system or, more generally, a matter-antimatter system.