On the nature of the Schmid transition in a resistively shunted Josephson junction

We study the phase diagram of a resistively shunted Josephson junction (RSJJ) in the framework of the boundary sine-Gordon model. Using the non-perturbative functional renormalization group (FRG) we find that the transition is not controlled by a single fixed point but by a line of fixed points, and compute the continuously varying critical exponent $\nu$. We argue that the conductance also varies continuously along the transition line. In contrast to the traditional phase diagram of the RSJJ – an insulating ground state when the shunt resistance $R$ is larger than $R_q=h\mathrm{/}(2e{)}^2$ and a superconducting one when $R<R_q$ – the FRG predicts the transition line in the plane $(\alpha ,E_J\mathrm{/}{E}_C)$ to bend in the region $\alpha =R_q\mathrm{/}R<1$ but we cannot discard the possibility of a vertical line at $\alpha =1$ ($E_J$ and $E_C$ denote the Josephson and charging energies of the junction, respectively). Our results regarding the phase diagram and the nature of the transition are compared with Monte Carlo simulations and numerical renormalization group results.