Arresting dynamics in hardcore spin models

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 ${\Delta }_{\mathrm{KT}}$. 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 ${\Delta }_{\mathrm{J}}>{\Delta }_{\mathrm{KT}}$. 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 $\Delta \to {\Delta }_{\mathrm{J}}$.

arXiv commentReplaced with published version

References in corpus (16)

• Theoretical perspective on the glass transition and amorphous materials
• Jamming at Zero Temperature and Zero Applied Stress: the Epitome of Disorder
• Mean field theory of hard sphere glasses and jamming
• The glass transition of dense fluids of hard and compressible spheres
• The two dimensional XY model at the transition temperature: A high precision Monte Carlo study
• Random close packing revisited: How many ways can we pack frictionless disks?
• Nature of excitations and defects in structural glasses
• Dynamic critical exponent of two-, three-, and four-dimensional XY models with relaxational and resistively shunted junction dynamics
• The Binder Cumulant at the Kosterlitz-Thouless Transition
• Transitions and crossover phenomena in fully frustrated XY systems
• Spin and chiral orderings of the antiferromagnetic XY model on the triangular lattice and their critical properties
• Spin-chirality decoupling and critical properties of a two-dimensional fully frustrated XY model
• Delocalization of two-dimensional random surfaces with hard-core constraints
• Bose Metal as a Disruption of the Berezinskii-Kosterlitz-Thouless Transition in 2D Superconductors
• Berezinskii-Kosterlitz-Thouless Transition with a Constraint Lattice Action
• From hard spheres to hard-core spins