Eur. Phys. J. B (2016) 89: 127
https://doi.org/10.1140/epjb/e2016-70171-x

Regular Article

A numerical study of planar arrays of correlated spin islands

¹ Dipartimento di Fisica, Sapienza Università di Roma, P. A. Moro 2, 00185 Roma, Italy
² Instituto de Biocomputación y Física de Sistemas Complejos (BIFI), 50018 Zaragoza, Spain
³ Dipartimento di Fisica, IPCF-CNR and INFN, Sapienza Università di Roma, P. A. Moro 2, 00185 Roma, Italy
⁴ Departamento de Física and Instituto de Computación Científica Avanzada (ICCAEx), Universidad de Extremadura, 06071 Badajoz, Spain

^a e-mail: andrea.maiorano@roma1.infn.it

Received: 17 March 2016
Received in final form: 5 April 2016
Published online: 18 May 2016

Abstract

We analyze a system of interacting islands of XY spins on a triangular lattice. This model has been introduced a few years ago by Eley et al. [Nat. Phys. 8, 59 (2012)] 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.