Simulation results for an interacting pair of resistively shunted Josephson junctions

TL;DR

This paper uses a new Monte Carlo algorithm to study the phase diagram and critical behavior of two interacting resistively shunted Josephson junctions, revealing three phases and confirming theoretical predictions.

Contribution

It introduces a novel cluster Monte Carlo method and a mean-field theory to analyze the phase transitions and critical properties of coupled Josephson junctions.

Findings

Three distinct phases identified in the system.

Critical resistance and exponents match single junction behavior.

New mean-field theory accurately predicts phase boundary.

Abstract

Using a new cluster Monte Carlo algorithm, we study the phase diagram and critical properties of an interacting pair of resistively shunted Josephson junctions. This system models tunneling between two electrodes through a small superconducting grain, and is described by a double sine-Gordon model. In accordance with theoretical predictions, we observe three different phases and crossover effects arising from an intermediate coupling fixed point. On the superconductor-to-metal phase boundary, the observed critical behavior is within error-bars the same as in a single junction, with identical values of the critical resistance and a correlation function exponent which depends only on the strength of the Josephson coupling. We explain these critical properties on the basis of a renormalization group (RG) calculation. In addition, we propose an alternative new mean-field theory for this transition, which correctly predicts the location of the phase boundary at intermediate Josephson coupling strength.