The nature and boundary of the floating phase in a dissipative Josephson junction array

TL;DR

This paper investigates the unique properties and phase transition mechanisms of dissipative Josephson junction arrays, revealing a continuous set of critical points governed by local lattice topology across various dimensions.

Contribution

It demonstrates that the transition into the floating phase is controlled by a line of critical fixed points determined solely by local lattice topology, in any spatial dimension.

Findings

Correlations in the floating phase are long-ranged in time, short-ranged in space.

The transition is governed by a continuous locus of fixed points.

The fixed points depend only on local lattice topology.

Abstract

We study the nature of correlations within, and the transition into, the floating phase of dissipative Josephson junction arrays. Order parameter correlations in this phase are long-ranged in time, but only short-ranged in space. A perturbative RG analysis shows that, in {\it arbitrary} spatial dimension, the transition is controlled by a continuous locus of critical fixed points determined entirely by the \textit{local} topology of the lattice. This may be the most natural example of a line of critical points existing in arbitrary dimensions.