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

TL;DR

This paper investigates a constrained statistical mechanics model related to superconducting device lattices, revealing a dynamical obstruction that prevents equilibration and leads to glassy behavior despite critical static properties.

Contribution

It introduces a variant of Baxter's 3-color model with local interactions, demonstrating how topological constraints cause dynamical freezing and phase transition phenomena in related superconducting lattice systems.

Findings

Critical line exists for ferromagnetic interactions with a first order transition.

Dynamical freezing occurs with domain walls of straight segments.

A dynamical temperature lower than the static critical temperature is identified.

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{kagom\'e} 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.