Second-order dynamic transition in a p=2 spin-glass model

TL;DR

This paper investigates the dynamics of a p=2 spin-glass model, revealing a second-order phase transition in dynamical activity within the low-temperature phase, with similar behavior observed in a 3D ferromagnet.

Contribution

It demonstrates the existence of a second-order dynamical phase transition in a p=2 spin-glass model using Ruelle's formalism and extends the findings to a related ferromagnetic model.

Findings

Dynamical phase transition is second-order in the spin-glass phase.

The transition separates active and inactive dynamical trajectories.

Similar dynamical behavior is observed in a 3D ferromagnet.

Abstract

We consider the dynamics of a disordered p-spin model with p=2, analyzing the dynamics within Ruelle's thermodynamic formalism, We use an indicator of the dynamical activity to construct the relevant dynamical Gibbs ensemble. We prove that the dynamics in the low-temperature (spin glass) phase of the model take place at a second-order phase transition between dynamically active and inactive trajectories. We also show that the same behaviour is found in a related model of a three-dimensional ferromagnet.