Arresting dynamics in hardcore spin models

TL;DR

This paper investigates the dynamics of hardcore spin models on lattices, revealing a divergence in relaxation time due to topological defect immobilization, and introduces protocols to understand nonadiabatic compression limits.

Contribution

It introduces a novel lattice spin model analogy to hard spheres, identifies a nonadiabatic compression limit, and explains the divergence in relaxation times via defect dynamics.

Findings

Nonadiabatic protocols fail to compress beyond a critical exclusion angle.

Relaxation times diverge algebraically near the critical angle.

Topological defects become immobile, causing slow dynamics.

Abstract

We study the dynamics of hardcore spin models on the square and triangular lattice, constructed by analogy to hard spheres, where the translational degrees of freedom of the spheres are replaced by orientational degrees of freedom of spins on a lattice and the packing fraction as a control parameter is replaced by an exclusion angle. In equilibrium, models on both lattices exhibit a Kosterlitz-Thouless transition at an exclusion angle $\Delta_{\rm KT}$. We devise compression protocols for hardcore spins and find that {\it any} protocol that changes the exclusion angle nonadiabatically, if endowed with only local dynamics, fails to compress random initial states beyond an angle $\Delta_{\rm J}> \Delta_{\rm KT}$. This coincides with a doubly algebraic divergence of the relaxation time of compressed states towards equilibrium. We identify a remarkably simple mechanism underpinning this divergent timescale: topological defects involved in the phase ordering kinetics of the system become incompatible with the hardcore spin constraint, leading to a vanishing defect mobility as $\Delta\rightarrow\Delta_{\rm J}$.