Phase transitions in a frustrated XY model with zig-zag couplings

TL;DR

This paper investigates a generalized frustrated XY model with zig-zag couplings, revealing complex phase transitions and critical behavior that interpolate between square and triangular lattice models, with implications for physical realizations like Josephson-junction arrays.

Contribution

It introduces a new zig-zag coupling pattern in the frustrated XY model and analyzes its phase diagram and critical phenomena, connecting it to the XY-Ising universality class.

Findings

Phase transitions depend on the coupling ratio ;

Transition line exhibits XY-Ising universality class with non-Ising critical exponents;

Model can be realized in Josephson-junction arrays under magnetic field.

Abstract

We study a new generalized version of the square-lattice frustrated XY model where unequal ferromagnetic and antiferromagnetic couplings are arranged in a zig-zag pattern. The ratio between the couplings $\rho$ can be used to tune the system, continuously, from the isotropic square-lattice to the triangular-lattice frustrated XY model. The model can be physically realized as a Josephson-junction array with two different couplings, in a magnetic field corresponding to half-flux quanta per plaquette. Mean-field approximation, Ginzburg-Landau expansion and finite-size scaling of Monte Carlo simulations are used to study the phase diagram and critical behavior. Depending on the value of $\rho$, two separate transitions or a transition line in the universality class of the XY-Ising model, with combined $Z_2$ and U(1) symmetries, takes place. In particular, the phase transitions of the standard square-lattice and triangular-lattice frustrated XY models correspond to two different cuts through the same transition line. Estimates of the chiral ($Z_2$) critical exponents on this transition line deviate significantly from the pure Ising values, consistent with that along the critical line of the XY-Ising model. This suggests that a frustrated XY model or Josephson-junction array with a zig-zag coupling modulation can provide a physical realization of the XY-Ising model critical line.