Abstract
We characterize the phase space for the infinite volume limit of a ferromagnetic mean-field XY model in a random field pointing in one direction with two symmetric values. We determine the stationary solutions and detect possible phase transitions in the interaction strength for fixed random field intensity. We show that at low temperature magnetic ordering appears perpendicularly to the field. The latter situation corresponds to a spin-flop transition.
Highlights
Synchronization processes are ubiquitous in nature and, in particular, are rooted in human life from the metabolic processes in our cells to the highest cognitive tasks we perform as a group of individuals
The paper is concerned with the study of the phase diagram for a mean-field planar XY model with external field
We first determined the N → +∞ limiting distribution on the path space by deriving an appropriate law of large numbers based on a large deviation principle
Summary
Synchronization processes are ubiquitous in nature and, in particular, are rooted in human life from the metabolic processes in our cells to the highest cognitive tasks we perform as a group of individuals. Flashing fireflies, chirping crickets, violinists playing in unison, applauding audiences, firings of neuron assemblies, pacemaker cell beats, etc. Are ensembles of units able to organize spontaneously allowing order to arise starting from disordered configurations [30,36]. Synchrony has attracted much interest in the last decades.
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