Phase transitions of frustrated XY models on deformed square lattices.

Abstract

We have studied both analytically and numerically the phase transitions in a novel type of Josephson-junction array in a magnetic field equal to one flux quantum per two lattice cells. The lattice we consider has two lattice constants, \ensuremath{\tau} and 1-\ensuremath{\tau}, in one direction and has one in the other. Monte Carlo simulation and mean-field calculations, as well as analytical arguments are performed which indicate that the phase transition is of the Kosterlitz-Thouless (KT) type for \ensuremath{\tau}\ensuremath{\le}${\ensuremath{\tau}}_{c}$\ensuremath{\sim}0.288. The ground-state configuration is found to be helically ordered with U(1) symmetry. In the interval ${\ensuremath{\tau}}_{c}$\ensuremath{\le}1/2, the ground state has double discrete degeneracy and the KT transition can be mixed with an Ising-type transition at special values of \ensuremath{\tau}. The variation of the transition temperature with magnetic field is also estimated. The behavior of the deformed square lattice at other field strengths, and in the presence of disorder, is discussed qualitatively.