Dynamical obstruction in a constrained system and its realization in lattices of superconducting devices

Abstract

Hard constraints imposed in statistical mechanics models can lead to interesting thermodynamical behaviors, but may at the same time raise obstructions in the thoroughfare to thermal equilibration. Here we study a variant of Baxter's 3-color model in which local interactions and defects are included, and discuss its connection to triangular arrays of Josephson junctions of superconductors and \textit{kagomé} networks of superconducting wires. The model is equivalent to an Ising model in a hexagonal lattice with the constraint that the magnetization of each hexagon is $\pm 6$ or 0. For ferromagnetic interactions, we find that the system is critical for a range of temperatures (critical line) that terminates when it undergoes an exotic first order phase transition with a jump from a zero magnetization state into the fully magnetized state at finite temperature. Dynamically, however, we find that the system becomes frozen into domains. The domain walls are made of perfectly straight segments, and domain growth appears frozen within the time scales studied with Monte Carlo simulations. This dynamical obstruction has its origin in the topology of the allowed reconfigurations in phase space, which consist of updates of closed loops of spins. As a consequence of the dynamical obstruction, there exists a dynamical temperature, lower than the (avoided) static critical temperature, at which the system is seen to jump from a ``supercooled liquid'' to a ``polycrystalline'' phase. In contrast, for antiferromagnetic interactions, we argue that the system orders for infinitesimal coupling because of the constraint, and we observe no interesting dynamical effects.

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• Heterogeneous freezing in a geometrically frustrated spin model without disorder: spontaneous generation of two time-scales
• Zero-temperature Kosterlitz-Thouless transition in a two-dimensional quantum system
• Quantum three-coloring dimer model and the disruptive effect of quantum glassiness on its line of critical points
• Fractal Quantum Phase Transitions: Critical Phenomena Beyond Renormalization
• Colorings of odd or even chirality on hexagonal lattices
• Frustrated colloidal ordering and fully packed loops in arrays of optical traps
• High-Temperature Criticality in Strongly Constrained Quantum Systems
• Geometric criticality between plaquette phases in integer-spin kagome XXZ antiferromagnets
• Multiple time scales from hard local constraints: glassiness without disorder
• Criticality of a classical dimer model on the triangular lattice
• Frustrated superconductivity and sextetting order
• Folding of the triangular lattice in a discrete three-dimensional space: Crumpling transitions in the negative-bending-rigidity regime
• Color-dependent interactions in the three coloring model
• Gauge symmetry and non-abelian topological sectors in a geometrically constrained model on the honeycomb lattice
• Invariants of winding-numbers and steric obstruction in dynamics of flux lines