Journal of Physics Conference Series

The dimensional crossover in critical behavior of layered XY-model

Ivan S Popov, Anna P Popova, Pavel Vladimirovich Prudnikov

Published Nov 1, 2019• 1 citation

Abstract

Abstract The study of critical properties and size transition in a diluted layered XY-model was carried out for the first time. The dimensional dependence of the temperature T BKT(p, N) of the Berezinskii-Kosterlitz-Thouless phase transition on the system thickness N is obtained for a diluted layered XY-model for a wide range of spin concentrations p. The temperature T, concentration p, and dimensional N dependencies of the vortex density v(p, N, T) in a layered XY-model are obtained.

DOI: 10.1088/1742-6596/1389/1/012025

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Journal of Physics Conference Series

The dimensional crossover in critical behavior of layered XY-model

Ivan S Popov, Anna P Popova, Pavel Vladimirovich Prudnikov

Published Nov 1, 2019• 1 citation

Publisher

Abstract

DOI: 10.1088/1742-6596/1389/1/012025

Related papers

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J_\parallel

and inter-plane

J_\perp

couplings. Our study includes very small values of the system anisotropy

Δ=J_\perp /J_\parallel

not studied before, and focuses on characterizing the crossover from quasi-2D topological scaling to genuine 3D critical behavior. The numerical results for the critical temperature unambiguously reveal a logarithmic scaling with

Δ

, directly related to the topological scaling in the 2D limit. Despite the 3D nature of the layered XY criticality, topological scaling signatures survive up to system sizes comparable to the crossover length

\ell_J

, which diverges at small

Δ

with a scaling behavior reminiscent of the Berezinskii-Kosterlitz-Thouless (BKT) transition. This shows that genuine 3D symmetry-breaking behavior emerges only at exceedingly large system sizes when the anisotropy is very strong. Our results indicate that new experimental evidence is required to clarify the extent to which the critical signatures observed in layered strongly correlated materials are shaped by their pronounced anisotropy.

Abstract The Berezinskii–Kosterlitz–Thouless (BKT) transition of the two-dimensional

XY

model on the honeycomb lattice is investigated using both the techniques of Neural network (NN) and Monte Carlo simulations. It is demonstrated in the literature that, with certain plausible assumptions, the associated critical temperature

T_{\text{BKT,H}}

is found to be

{1}/{\sqrt{2}}

exactly. Surprisingly, the value of

T_{\text{BKT,H}}

obtained from our NN calculations is 0.572(3), which deviates significantly from

{1}/{\sqrt{2}}

. In addition, based on the helicity modulus, the

T_{\text{BKT,H}}

determined is 0.576(4), agreeing well with that resulting from the NN estimation. It will be interesting to carry out a more detailed analytic calculation to obtain a theoretical value consistent with the numerical result reached here.