Essential finite-size effect in the 2D XY model
S.G. Chung
TL;DR
This paper investigates the finite-size effects and phase transition behavior of the 2D XY model using transfer matrix and renormalization group methods, revealing an essential finite-size effect and a finite-system BKT transition.
Contribution
It introduces a detailed analysis of finite-size effects in the 2D XY model and identifies the finite-system BKT transition temperature using advanced computational methods.
Findings
Finite-size effects are essential in the 2D XY model.
A BKT transition appears in finite systems of 2000-3000 spins.
The effective critical temperature is approximately 1.07.
Abstract
The thermodynamics of the 2D XY model is formulated by a transfer matrix method and analyzed by a density matrix renormalization group. The finite-size scaling and the beta function of the model are studied by the Roomany-Wyld renormalization group theory. It is found that the 2D XY model has an essential finite-size effect and the Berezinskii-Kosterlitz-Thouless transition with the critical temperature TBKT = 0.892 appears in a finite system of 2000 - 3000 spins as a massless to massive transition with the effective critical temperature Tc = 1.07 " 0.01.
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