A numerical study of planar arrays of correlated spin islands

TL;DR

This paper numerically investigates a system of correlated XY spin islands on a triangular lattice, revealing two temperature-driven crossovers and a phase transition in the Ising universality class related to global coherence.

Contribution

It provides a detailed numerical analysis of a mesoscopic spin island model, connecting local and global interactions to experimental phenomena in superconductor-normal metal-superconductor arrays.

Findings

Identification of two temperature crossovers corresponding to local and global coherence

The global coherence transition belongs to the Ising universality class

The transition depends on island spacing and proximity effects

Abstract

We present our analysis of a system of interacting islands of XY spins on a triangular lattice that has been introduced a few years ago by Eley et al. to account for the phenomenology in experiments on tunable arrays of proximity coupled long superconductor-normal metal-superconductor junctions. The main features of the model are the separation of a local and a global interaction energy scale and the mesoscopic character of the spin islands. Upon lowering the temperature the model undergoes two crossovers corresponding to an increasing phase coherence on a single island and to the onset of global coherence across the array; the latter is a thermodynamical phase transition in the Ising universality class. The dependence of the second transition on the island edge-to-edge spacing is related to the proximity-effect of the coupling constant.