Phase diagram of the lattice superconductor

Abstract

In a mean-field approximation the phase transition of a lattice superconductor is understood in terms of an orientation of its topological excitations (vortex loops and magnetic field loops). The loops are obtained through a duality transformation of the original variables. The phase boundary T_c(e²,b⁻¹) is found as a function of the charge e and a Ginzburg-Landau quartic term coefficient b. Second-order behavior is found for a region b > b_c(e²) and a tricritical point with first-order behavior appears for b < b_c(e²), consistent with the Monte Carlo results of Dasgupta and Halperin and of Bartholomew. A crossover between XY and inverted XY behavior, in the second-order regime, is conjectured. An outer first-order phase boundary T_HLM(e²,b⁻¹)≳T_c(e², b⁻¹) is also found, consistent with the early continuum results of Halperin, Lubensky, and Ma (HLM). T_HLM(e²,b⁻¹) is associated with ordering within a superconducting grain, while T_c(e²,b⁻¹) involves phase locking between grains.