Out of equilibrium dynamics of the spiral model

TL;DR

This paper investigates the out-of-equilibrium relaxation dynamics of the two-dimensional spiral model, revealing finite-time decorrelation of unblocked states and similarities to one-dimensional coarsening phenomena.

Contribution

It demonstrates that unblocked states fully decorrelate in finite times regardless of phase, and links the dynamics to coarsening with vacancy lines, providing new insights into kinetic constraints.

Findings

Unblocked states decorrelate in finite times.

Dynamics resemble coarsening in 1D Ising model.

Observable behaviors support the coarsening analogy.

Abstract

We study the relaxation of the bi-dimensional kinetically constrained spiral model. We show that due to the reversibility of the dynamic rules any unblocked state fully decorrelates in finite times irrespectively of the system being in the unjammed or the jammed phase. In consequence, the evolution of any unblocked configuration occurs in a different sector of phase space from the one that includes the equilibrium blocked equilibrium configurations at criticality and in the jammed phase. We argue that such out of equilibrium dynamics share many points in common with coarsening in the one-dimensional Ising model and we identify the coarsening structures that are, basically, lines of vacancies. We provide evidence for this claim by analyzing the behaviour of several observables including the density of particles and vacancies, the spatial correlation function, the time-dependent persistence and the linear response.