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AIP conference proceedings

Glassy dynamics of a two-dimensional non-disordered spin model

Juan P. Garrahan

Published Jan 1, 2001• 1 citation
Publisher

Abstract

We study the low temperature dynamics of a two dimensional spin system, which displays glassiness despite the absence of disorder or frustration, and is an explicit realization of the “hierarchically constrained dynamics” scenario for glassy systems. We solve exactly the statics of the model, and study in detail the dynamical behavior of one-time and two-time quantities.

DOI
10.1063/1.1358159

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We study the low temperature dynamics of a two dimensional spin system, which displays glassiness despite the absence of disorder or frustration, and is an explicit realization of the “hierarchically constrained dynamics” scenario for glassy systems. We solve exactly the statics of the model, and study in detail the dynamical behavior of one-time and two-time quantities.
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We introduce a class of dissipative quantum spin models with local interactions and without quenched disorder that show glassy behavior. These models are the quantum analogs of the classical facilitated spin models. Just like their classical counterparts, quantum facilitated models display complex glassy dynamics despite the fact that their stationary state is essentially trivial. In these systems, dynamical arrest is a consequence of kinetic constraints and not of static ordering. These models display a quantum version of dynamic heterogeneity: the dynamics toward relaxation is spatially correlated despite the absence of static correlations. Associated dynamical fluctuation phenomena such as decoupling of time scales is also observed. Moreover, we find that close to the classical limit, quantum fluctuations can enhance glassiness, as recently reported for quantum liquids.
We show that applying simple dynamical rules to Baxter's eight-vertex model leads to a system which resembles a glass-forming liquid. There are analogies with liquid, supercooled liquid, glassy, and crystalline states. The disordered phases exhibit strong dynamical heterogeneity at low temperatures, which may be described in terms of an emergent mobility field. Their dynamics are well described by a simple model with trivial thermodynamics, but an emergent kinetic constraint. We show that the (second order) thermodynamic transition to the ordered phase may be interpreted in terms of confinement of the excitations in the mobility field. We also describe the aging of disordered states toward the ordered phase, in terms of simple rate equations.
We introduce a Potts model with quenched, frustrated disorder, which enjoys a gauge symmetry that forbids spontaneous magnetization and allows the glassy phase to extend from Tc{T}_{c}Tc​ down to T=0.T=0.T=0. We study numerically the four-dimensional model with q=4q=4q=4 states. We show the existence of a glassy phase, and we characterize it by studying the probability distributions of an order parameter, the binder cumulant, and the divergence of the overlap susceptibility. We show that the dynamical behavior of the system is characterized by aging.
We present a lattice spin model that mimics a system of interacting particles through a short-range repulsive potential and a long-range attractive power-law decaying potential. We perform a detailed analysis of the general equilibrium phase diagram of the model at finite temperature, showing that the only possible equilibrium phases are the ferromagnetic and the antiferromagnetic ones. We then study the nonequilibrium behavior of the model after a quench to subcritical temperatures, in the antiferromagnetic region of the phase diagram region, where the pair interaction potential behaves in the same qualitative way as in a Lennard-Jones gas. We find that even in the absence of quenched disorder or geometric frustration, the competition between interactions gives rise to nonequilibrium disordered structures at low enough temperatures that strongly slow down the relaxation of the system. This nonequilibrium state presents several features characteristic of glassy systems such as subaging, nontrivial fuctuation dissipation relations, and possible logarithmic growth of free-energy barriers to coarsening.
In this thesis we investigate the Renormalization Group (RG) approach in finite-dimensional glassy systems, whose critical features are still not well-established, or simply unknown. We focus on spin and structural-glass models built on hierarchical lattices, which are the simplest non-mean-field systems where the RG framework emerges in a natural way. The resulting critical properties shed light on the critical behavior of spin and structural glasses beyond mean field, and suggest future directions for understanding the criticality of more realistic glassy systems.