Spontaneous symmetry breaking in finite systems and anomalous order-parameter correlations

TL;DR

This paper defines spontaneous symmetry breaking in finite systems using jump probabilities in Ising models, revealing an interval where symmetry breaks and highlighting anomalous auto-correlation enhancements linked to intermittency transitions.

Contribution

It introduces a finite-system definition of spontaneous symmetry breaking based on jump probabilities and identifies an anomalous auto-correlation behavior during the symmetry-breaking process.

Findings

Existence of a temperature interval for symmetry breaking in finite systems.

Identification of a pseudocritical point where symmetric and non-symmetric states bifurcate.

Observation of maximal auto-correlation times linked to intermittency transition.

Abstract

We show that the spontaneous symmetry breaking can be defined also for finite systems based on the properly defined jump probability between the ground states in the 2d and 3d Ising models on a square and a cubic lattice respectively. Our analysis reveals the existence of an interval in the temperature (control parameter) space within which the spontaneous symmetry breaking takes place. The upper limit of this region is the pseudocritical point where the symmetric vacuum bifurcates in energetically degenerate non-symmetric vacua, initiating the spontaneous symmetry breaking process. The lower limit, identified as the temperature value at which the spontaneous symmetry breaking is completed, is characterized by maximal characteristic time for the decay of magnetization (order parameter) auto-correlations. We argue that this anomalous enhancement of auto-correlations is attributed to the transition from type I to on-off intermittency in the order parameter dynamics. Possible phenomenological implications of this behaviour are briefly discussed.