Random pinning in glassy spin models with plaquette interactions

TL;DR

This study investigates how random pinning affects amorphous order in glassy spin models with plaquette interactions, revealing a sharp crossover from relaxation to localization without a phase transition, and highlighting the role of length and time scales.

Contribution

It introduces a finite-dimensional model analysis showing that random pinning causes a sharp dynamical crossover, differing from mean-field and other theoretical approaches.

Findings

Sharp crossover from bulk relaxation to localization with increased pinned spins

Scaling behavior observed at low temperatures in the models

Finite-dimensional effects differ from mean-field predictions

Abstract

We use a random pinning procedure to study amorphous order in two glassy spin models. On increasing the concentration of pinned spins at constant temperature, we find a sharp crossover (but no thermodynamic phase transition) from bulk relaxation to localisation in a single state. At low temperatures, both models exhibit scaling behaviour. We discuss the growing length and time scales associated with amorphous order, and the fraction of pinned spins required to localize the system in a single state. These results, obtained for finite dimensional interacting models, provide a theoretical scenario for the effect of random pinning that differs qualitatively from previous approaches based either on mean-field, mode-coupling, or renormalization group reatments.