Phase and Vortex Correlations in Superconducting Josephson-Junction Arrays at Irrational Magnetic Frustration

Phase coherence and vortex order in a Josephson-junction array at irrational frustration are studied by extensive Monte Carlo simulations using the parallel-tempering method. A scaling analysis of the correlation length of phase variables in the full equilibrated system shows that the critical temperature vanishes with a power-law divergent correlation length and critical exponent ${\nu }_{\mathrm{ph}}$, in agreement with recent results from resistivity scaling analysis. A similar scaling analysis for vortex variables reveals a different critical exponent ${\nu }_v$, suggesting that there are two distinct correlation lengths associated with a decoupled zero-temperature phase transition.

Figure 1

Trajectory in temperature space of a replica starting at temperature $T=0.30$, for system size $L=55$. The simulation included 100 replicas in the range $T=0.30$ to $T=0.096$.

Figure 2

Scaled correlation length of phase variables ${\xi }_{\mathrm{ph}}/L$ for different system sizes $L$. Inset: Scaling plot according to Eq. (3), assuming $T_c=0$ with ${\nu }_{\mathrm{ph}}=1.2$.

Figure 3

Scaled correlation length of vortex variables ${\xi }_v/L$ for different system sizes $L$.

Figure 4

Scaling plot according to Eq. (3), assuming $T_c=0$, for the vortex correlation length ${\xi }_v$, with ${\nu }_v=2.2$.