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

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

1997-01-06

arxiv.org/abs/cond-mat/9701022v1

Phys. Rev. B 55, 8361 (97).

Physics

Condensed Matter

Statistical Mechanics

11 pages, 9 figures, RevTex, to appear in Phys. Rev. B

Scientific paper

10.1103/PhysRevB.55.8361

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.

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