Kosterlitz-Thouless Transition: The Diluted XY model

Abstract

Abstract. The effect of nonmagnetic disorder on Berezinskii-Kosterlitz-Thouless (BKT) transition in the two-dimensional ferromagnetic XY model on a square lattice, diluted by randomly placed vacancies can be an important source of information on the role played by vortexes in this transition. The transition temperature TBKT is determined as a function of vacancy density ρv by stiffness ρ and for different size of the lattice. The anomalous behavior for TBKT when ρv is close to the square lattice percolation limit is a consequence of the effect of finite size of lattice and not due the quantum fluctuations as concluded in literature. We obtain that TBKT falls to zero at ρv ≈ 0.40 close to the value 0.41 obtained for the classic model.

Uniformly Frustrated XY Model: Strengthening of the Vortex Lattice by Intrinsic Disorder

“…From a theoretical perspective, one possible way to investigate such interplay is by studying the classical XY model in the presence of both disorder and transverse magnetic field. As an effective model for superconducting phase fluctuations, the 2D XY model has been applied to the study of disordered and inhomogeneous SC films over the years [15][16][17][18][19][20][21][22][23][24] as well as to the 2D vortex lattice melting for different values of the applied magnetic field [25][26][27][28][29][30][31][32]. The combined effect of quenched disorder and transverse magnetic field has been so far addressed by including in the XY model spatially random quenched magnetic fluxes, but with a resulting zero net magnetic field [2,15,33,34].…”