We examine the Kosterlitz-Thouless universality class and show that essential scaling at this type of phase transition is not self-consistent unless multiplicative logarithmic corrections are included. In the case of specific heat these logarithmic corrections are identified analytically. To identify those corresponding to the susceptibility we set up a numerical method involving the finite-size scaling of Lee-Yang zeroes. We also study the density of zeroes and introduce a new concept called index scaling. We apply the method to the XY model and the c]osely related step model in two dimensions. The critical parameters (including logarithmic corrections) of the step model are compatible with those of the XY model indicating that both models belong to the same universality class. This result then raises questions over how a vortex binding scenario can be the driving mechanism for the phase transition. Furthermore, the logarithmic corrections identified numerically by our methods of fitting are not in agreement with the renormalization group predictions of Kosterlitz and Thouless.We examine the Kosterlitz-Thouless universality class and show that essential scaling at this type of phase transition is not self-consistent unless multiplicative logarithmic corrections are included. In the case of specific heat these logarithmic corrections are identified analytically. To identify those corresponding to the susceptibility we set up a numerical method involving the finite-size scaling of Lee-Yang zeroes. We also study the density of zeroes and introduce a new concept called index scaling. We apply the method to the XY model and the c]osely related step model in two dimensions. The critical parameters (including logarithmic corrections) of the step model are compatible with those of the XY model indicating that both models belong to the same universality class. This result then raises questions over how a vortex binding scenario can be the driving mechanism for the phase transition. Furthermore, the logarithmic corrections identified numerically by our methods of fitting are not in agreement with the renormalization group predictions of Kosterlitz and Thouless.

Jan 1, 199747 citations

The Blume-Capel universality class

Alessandro Codello, Mahmoud Safari, Gian Paolo Vacca +1 more

Jun 21, 20170 citations

Getting the jump in the Kosterlitz–Thouless transition

Christopher J. Lobb

WORLD SCIENTIFIC eBooksAug 14, 20180 citations

New Ordered Phases in a Class of Generalized XY Models

Fábio Campos Poderoso, Jeferson J. Arenzon, Yan Levin

It is well known that the 2D XY model exhibits an unusual infinite order phase transition belonging to the Kosterlitz-Thouless (KT) universality class. Introduction of a nematic coupling into the XY Hamiltonian leads to an additional phase transition in the Ising universality class [D. H. Lee and G. Grinstein, Phys. Rev. Lett. 55, 541 (1985)]. Using a combination of extensive Monte Carlo simulations and finite size scaling, we show that the higher order harmonics lead to a qualitatively different phase diagram, with additional ordered phases originating from the competition between the ferromagnetic and pseudonematic couplings. The new phase transitions belong to the 2D Potts, Ising, or KT universality classes.It is well known that the 2D XY model exhibits an unusual infinite order phase transition belonging to the Kosterlitz-Thouless (KT) universality class. Introduction of a nematic coupling into the XY Hamiltonian leads to an additional phase transition in the Ising universality class [D. H. Lee and G. Grinstein, Phys. Rev. Lett. 55, 541 (1985)]. Using a combination of extensive Monte Carlo simulations and finite size scaling, we show that the higher order harmonics lead to a qualitatively different phase diagram, with additional ordered phases originating from the competition between the ferromagnetic and pseudonematic couplings. The new phase transitions belong to the 2D Potts, Ising, or KT universality classes.

arXiv:1008.0868Physical Review LettersFeb 10, 201157 citations

Berezinskii-Kosterlitz-Thouless Transition

Pedro D Sacramento

Springer eBooksJan 1, 20250 citations

Signatures of the Berezinskii-Kosterlitz-Thouless transition on the location of the zeros of the canonical partition function for the 2D XY-model

J. C. S. Rocha, L. A. S. Mόl, B. V. Costa

In this work we show how one can use the zeros of the canonical partition function, the Fisher zeros, to unambiguously characterize a transition as being in the Berezinskii-Kosterlitz-Thouless ( $BKT$ ) class of universality. By studying the zeros map for the 2D XY-model, we found that its internal border coalesces into the real positive axis in a finite region corresponding to temperatures smaller than the $BKT$ transition temperature. This behavior is consistent with the predicted existence of a line of critical points below the transition temperature, allowing one to distinguish the $BKT$ class of universality from other possibilities.In this work we show how one can use the zeros of the canonical partition function, the Fisher zeros, to unambiguously characterize a transition as being in the Berezinskii-Kosterlitz-Thouless ($BKT$) class of universality. By studying the zeros map for the 2D XY-model, we found that its internal border coalesces into the real positive axis in a finite region corresponding to temperatures smaller than the $BKT$ transition temperature. This behavior is consistent with the predicted existence of a line of critical points below the transition temperature, allowing one to distinguish the $BKT$ class of universality from other possibilities.

Jul 8, 20150 citations

In this work we show how one can use the zeros of the canonical partition function, the Fisher zeros, to unambiguously characterize a transition as being in the Berezinskii-Kosterlitz-Thouless (

BKT

) class of universality. By studying the zeros map for the 2D XY-model, we found that its internal border coalesces into the real positive axis in a finite region corresponding to temperatures smaller than the

BKT

transition temperature. This behavior is consistent with the predicted existence of a line of critical points below the transition temperature, allowing one to distinguish the

BKT

class of universality from other possibilities.