Glassy dynamics and aging in an exactly solvable spin model

TL;DR

This paper presents an exactly solvable two-dimensional spin model exhibiting glassy dynamics and aging behavior without disorder, providing insights into non-traditional glassy systems.

Contribution

The authors introduce a homogeneous, short-range interaction spin model that displays glassy behavior and aging, with exact solutions for static and dynamic properties.

Findings

Exact solution for the partition function and energy barriers.

Simulation results agree with analytical predictions.

Model exhibits aging and falls out of equilibrium without a sharp glass transition.

Abstract

We introduce a simple two-dimensional spin model with short-range interactions which shows glassy behavior despite a Hamiltonian which is completely homogeneous and possesses no randomness. We solve exactly for both the static partition function of the model and the distribution of energy barriers, giving us the equilibration time-scales at low temperature. Simulations of instantaneous quenches and of annealing of the model are in good agreement with the analytic calculations. We also measure the two-time spin correlation as a function of waiting time, and show that the model has aging behavior consistent with the distribution of barrier heights. The model appears to have no sharp glass transition. Instead, it falls out of equilibrium at a temperature which decreases logarithmically as a function of the cooling time.