Universality class of the mode-locked glassy random laser

TL;DR

This study uses GPU-accelerated Monte Carlo simulations to analyze the critical behavior of a spin-glass-like model for mode-locked glassy random lasers, revealing its mean-field universality class and signs of replica symmetry breaking.

Contribution

It identifies the universality class of the mode-locked glassy random laser and characterizes the phase transition and low-temperature phase using finite size scaling and overlap distribution analysis.

Findings

The mode-locked random laser belongs to a mean-field universality class.

Critical points and indices of the phase transition are identified.

Evidence of replica symmetry breaking in the lasing regime.

Abstract

By means of enhanced Monte Carlo numerical simulations parallelized on GPU's we study the critical properties of the spin-glass-like model for the mode-locked glassy random laser, a $4$-spin model with complex spins with a global spherical constraint and quenched random interactions. Using two different boundary conditions for the mode frequencies we identify the critical points and the critical indices of the random lasing phase transition using , with finite size scaling techniques. The outcome of the scaling analysis is that the mode-locked random laser is in a mean-field universality class, though different from the mean-field class of the Random Energy Model and the glassy random laser in the narrow band approximation, that is, the fully connected version of the present model. The low temperature (high pumping) phase is finally characterized by means of the overlap distribution and evidence for the onset of replica symmetry breaking in the lasing regime is provided.