Influence of quenched dilution on the quasi-long-range ordered phase of the $\mathsf{2d}$ $\mathsf{XY}$ model

Abstract

The influence of non magnetic impurities in the 2d XY model is investigated through Monte Carlo (MC) simulations. The general picture of the transition is fully understood from the Harris criterion which predicts that the universality class is unchanged, and the Berezinskii-Kosterlitz-Thouless description of the topological transition remains valid. We nevertheless address here the question about the influence of dilution on the quasi-long-range order at low temperatures. In particular, we study the asymptotic of the pair correlation function and report the MC estimates for the critical exponent η at different dilutions. In the weak dilution region, our MC calculations are further supported by simple spin-wave-like calculations.

Berezinskii-Kosterlitz-Thouless transition in two-dimensional lattice gas models

“…Moreover, a BKTLT may still survive if µ is negative but not too large in magnitude; this conjecture is supported by RG studies for the LG-PR 17,18,19 , and was confirmed by the simulation results obtained in Ref. 15 ; it also agrees with the conclusions of references 22,23,24,25 for two-dimensional magnets with quenched dilution; for large negative µ, the named RG treatments predict phase separation, i.e. a first-order transition between a BKT and a paramagnetic phase, and eventually the disappearance of the BKT phase.…”

Triangular Antiferromagnet with Nonmagnetic Impurities

“…In particular, the Berezinskii-Kostelitz-Thouless (BKT) transition formally has ¼ 1 and remains unaffected by vacancies as was confirmed numerically in [34]. The second-order transition into the uud state, which belongs to the universality class of the 2D three-state Potts model, has ¼ 1=3 and is, therefore, driven by impurities to a new random fixed point, see [35,36] and references therein.…”

Relaxational processes in the one-dimensional Ising model with long-range interactions

“…While, in this paper, the Edwards-Anderson (EA) order parameter [25] [Eq. (20)] is employed as a macroscopic variable to investigate dynamical properties, the droplet theory gives the time-delayed correlation of a local spin variable. The EA order parameter measures a similarity between replicated systems which have the same set of interactions {J ij }.…”

“…On the other hand, the critical exponent α is zero when σ = 2 and σ ≤ 3/2, and the dilution will be irrelevant to the universality class. For systems that exhibit the KT transition, it will not be a trivial question whether the dilution alters the universality class or not, but it seems irrelevant regarding numerical studies of the two-dimensional diluted XY model [20,21].…”