arXiv:2406.04059 · Physical review. B./Physical review. B

First-order and Berezinskii-Kosterlitz-Thouless phase transitions in two-dimensional generalized XY models

P. A. da Silva, R. J. C. Lopes, A. R. Pereira

Published Sep 24, 2024• 1 citation

Abstract

Besides the Berezinskii-Kosterlitz-Thouless phase transition, the two-dimensional generalized XY model, identified by a generalization parameter $q$ (as proposed by Romano and Zagrebnov), can also support a first-order phase transition, starting from a critical value ${q}_{c}$. However, the value of ${q}_{c}$ at which this transition takes place is unknown. In this paper, we take two approaches to accurately determine the critical parameter ${q}_{c}$. Furthermore, we show that the model is characterized by three distinct regions concerning both first-order and Berezinskii-Kosterlitz-Thouless phase transitions. Finally, the underlying mechanism governing such transitions is presented, along with an estimation of the critical temperatures.

DOI: 10.1103/physrevb.110.104112

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arXiv:2406.04059 · Physical review. B./Physical review. B

First-order and Berezinskii-Kosterlitz-Thouless phase transitions in two-dimensional generalized XY models

P. A. da Silva, R. J. C. Lopes, A. R. Pereira

Published Sep 24, 2024• 1 citation

arXiv HTML PDF

Abstract

Besides the Berezinskii-Kosterlitz-Thouless phase transition, the two-dimensional generalized XY model, identified by a generalization parameter

q

(as proposed by Romano and Zagrebnov), can also support a first-order phase transition, starting from a critical value

{q}_{c}

. However, the value of

{q}_{c}

at which this transition takes place is unknown. In this paper, we take two approaches to accurately determine the critical parameter

{q}_{c}

. Furthermore, we show that the model is characterized by three distinct regions concerning both first-order and Berezinskii-Kosterlitz-Thouless phase transitions. Finally, the underlying mechanism governing such transitions is presented, along with an estimation of the critical temperatures.

DOI: 10.1103/physrevb.110.104112

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Besides the Berezinskii-Kosterlitz-Thouless phase transition, the two-dimensional generalized XY model, identified by a generalization parameter

q

(as proposed by Romano and Zagrebnov), can also support a first-order phase transition, starting from a critical value

{q}_{c}

. However, the value of

{q}_{c}

at which this transition takes place is unknown. In this paper, we take two approaches to accurately determine the critical parameter

{q}_{c}

We study the two-dimensional generalized XY model that depends on an integer

q

by the Monte Carlo method. This model was recently proposed by Romano and Zagrebnov. We find a single Kosterlitz-Thouless (KT) transition for all values of

q

, in contrast with the previous speculation that there may be two transitions, one a regular KT transition and another a first-order transition at a higher temperature. We show the universality of the KT transitions by comparing the universal finite-size scaling behaviors at different values of

q

without assuming a specific universal form in terms of the KT transition temperature

T_{\rm KT}

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.