Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

Results in Physics

Berezinskii–Kosterlitz–Thouless Transition – A Universal Neural Network Study with Benchmarks

Y.-H. Tseng, Fu-Jiun Jiang

Published Jan 1, 2021• 7 citations
Publisher

Abstract

Using a supervised neural network (NN) trained once on a one-dimensional lattice of 200 sites, we calculate the Berezinskii–Kosterlitz–Thouless phase transitions of the two-dimensional (2D) classical XY and the 2D generalized classical XY models. In particular, both the bulk quantities Binder ratios and the spin states of the studied systems are employed to construct the needed configurations for the NN prediction. By applying semiempirical finite-size scaling to the relevant data, the critical points obtained by the NN approach agree well with the known results established in the literature. This implies that for each of the considered models, the determination of its various phases requires only a little information. The outcomes presented here demonstrate convincingly that the employed universal NN is not only valid for the symmetry breaking related phase transitions, but also works for calculating the critical points of the phase transitions associated with topology. The efficiency of the used NN in the computation is examined by carrying out several detailed benchmark calculations.

DOI
10.1016/j.rinp.2021.105134

Related papers

Berezinskii--Kosterlitz--Thouless transition -- a universal neural network study with benchmarking

Y.-H. Tseng, Fu-Jiun Jiang

Using a supervised neural network (NN) trained once on a one-dimensional lattice of 200 sites, we calculate the Berezinskii--Kosterlitz--Thouless phase transitions of the two-dimensional (2D) classical $XY$ and the 2D generalized classical $XY$ models. In particular, both the bulk quantities Binder ratios and the spin states of the studied systems are employed to construct the needed configurations for the NN prediction. By applying semiempirical finite-size scaling to the relevant data, the critical points obtained by the NN approach agree well with the known results established in the literature. This implies that for each of the considered models, the determination of its various phases requires only a little information. The outcomes presented here demonstrate convincingly that the employed universal NN is not only valid for the symmetry breaking related phase transitions, but also works for calculating the critical points of the phase transitions associated with topology. The efficiency of the used NN in the computation is examined by carrying out several detailed benchmark calculations.

arXiv:2110.01344•Oct 4, 2021•0 citations

Berezinskii–Kosterlitz–Thouless Transition of the Two-Dimensional XY Model on the Honeycomb Lattice

Fu-Jiun Jiang

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.

Progress of Theoretical and Experimental Physics•Sep 26, 2024•4 citations

A universal neural network for learning phases and criticalities

D.-R. Tan, J.-H. Peng, Y.-H. Tseng +1 more

A universal supervised neural network (NN) relevant to compute the associated criticalities of real experiments studying phase transitions is constructed. The validity of the built NN is examined by applying it to calculate the criticalities of several three-dimensional (3D) models on the cubic lattice, including the classical $O(3)$ model, the 5-state ferromagnetic Potts model, and a dimerized quantum antiferromagnetic Heisenberg model. Particularly, although the considered NN is only trained one time on a one-dimensional (1D) lattice with 120 sites, yet it has successfully determined the related critical points of the studied 3D systems. Moreover, real configurations of states are not used in the testing stage. Instead, the employed configurations for the prediction are constructed on a 1D lattice of 120 sites and are based on the bulk quantities or the microscopic states of the considered models. As a result, our calculations are ultimately efficient in computation and the applications of the built NN is extremely broaden. Considering the fact that the investigated systems vary dramatically from each other, it is amazing that the combination of these two strategies in the training and the testing stages lead to a highly universal supervised neural network for learning phases and criticalities of 3D models. Based on the outcomes presented in this study, it is favorably probable that much simpler but yet elegant machine learning techniques can be constructed for fields of many-body systems other than the critical phenomena.

arXiv:2103.10846•Mar 19, 2021•1 citation

Berezinskii--Kosterlitz--Thouless transition of the two-dimensional $XY$ model on the honeycomb lattice

Fu-Jiun Jiang

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 $\frac{1}{\sqrt{2}}$ exactly. Surprisingly, the value of $T_{\text{BKT,H}}$ obtained from our NN calculations is 0.560(9) which deviates significantly from $\frac{1}{\sqrt{2}}$. In addition, based on the helicity modulus, the $T_{\text{BKT,H}}$ determined is 0.571(8) agreeing well with that resulting from the NN estimation. The outcomes presented in this study indicate that a detailed analytic calculation is desirable to solve the found discrepancy.

arXiv:2406.14812•Jun 21, 2024•0 citations

Machine learning phases and criticalities without using real data for training

D.-R. Tan, Fu-Jiun Jiang

We study the phase transitions of three-dimensional (3D) classical $O(3)$ model and two-dimensional (2D) classical XY model, as well as both the quantum phase transitions of 2D and 3D dimerized spin-1/2 antiferromagnets, using the technique of supervised neural network (NN). Moreover, unlike the conventional approaches commonly used in the literature, the training sets employed in our investigation are neither the theoretical nor the real configurations of the considered systems. Remarkably, with such an unconventional set up of the training stage in conjunction with some semiexperimental finite-size scaling formulas, the associated critical points determined by the NN method agree well with the established results in the literature. The outcomes obtained here imply that certain unconventional training strategies, like the one used in this study, are not only cost-effective in computation but are also applicable for a wide range of physical systems.

arXiv:2007.14809•Physical review. B./Physical review. B•Dec 28, 2020•12 citations

Neural network evidence of a weakly first order phase transition for the two-dimensional 5-state Potts model

Yuan-Heng Tseng, Y.-H. Tseng, Fu-Jiun Jiang

A universal (supervised) neural network (NN), which is only trained once on a one-dimensional lattice of 200 sites, is employed to study the phase transition of the two-dimensional (2D) 5-state ferromagnetic Potts model on the square lattice. In particular, the NN is obtained by using merely two artificially made configurations as the training set. Due to the elegant features of the considered NN, results associated with systems consisting of over 4000000 spins can be obtained with ease, and convincing evidence showing the investigated phase transition is weakly first order is reached. The outcomes demonstrated here can hardly be achieved with the standard NNs that are commonly used in the literature.

arXiv:2111.14063•Nov 28, 2021•0 citations
Using a supervised neural network (NN) trained once on a one-dimensional lattice of 200 sites, we calculate the Berezinskii–Kosterlitz–Thouless phase transitions of the two-dimensional (2D) classical XY and the 2D generalized classical XY models. In particular, both the bulk quantities Binder ratios and the spin states of the studied systems are employed to construct the needed configurations for the NN prediction. By applying semiempirical finite-size scaling to the relevant data, the critical points obtained by the NN approach agree well with the known results established in the literature. This implies that for each of the considered models, the determination of its various phases requires only a little information. The outcomes presented here demonstrate convincingly that the employed universal NN is not only valid for the symmetry breaking related phase transitions, but also works for calculating the critical points of the phase transitions associated with topology. The efficiency of the used NN in the computation is examined by carrying out several detailed benchmark calculations.
Using a supervised neural network (NN) trained once on a one-dimensional lattice of 200 sites, we calculate the Berezinskii--Kosterlitz--Thouless phase transitions of the two-dimensional (2D) classical XYXYXY and the 2D generalized classical XYXYXY models. In particular, both the bulk quantities Binder ratios and the spin states of the studied systems are employed to construct the needed configurations for the NN prediction. By applying semiempirical finite-size scaling to the relevant data, the critical points obtained by the NN approach agree well with the known results established in the literature. This implies that for each of the considered models, the determination of its various phases requires only a little information. The outcomes presented here demonstrate convincingly that the employed universal NN is not only valid for the symmetry breaking related phase transitions, but also works for calculating the critical points of the phase transitions associated with topology. The efficiency of the used NN in the computation is examined by carrying out several detailed benchmark calculations.
Abstract The Berezinskii–Kosterlitz–Thouless (BKT) transition of the two-dimensional XYXYXY 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 TBKT,HT_{\text{BKT,H}}TBKT,H​ is found to be 1/2{1}/{\sqrt{2}}1/2​ exactly. Surprisingly, the value of TBKT,HT_{\text{BKT,H}}TBKT,H​ obtained from our NN calculations is 0.572(3), which deviates significantly from 1/2{1}/{\sqrt{2}}1/2​. In addition, based on the helicity modulus, the TBKT,HT_{\text{BKT,H}}TBKT,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.
A universal supervised neural network (NN) relevant to compute the associated criticalities of real experiments studying phase transitions is constructed. The validity of the built NN is examined by applying it to calculate the criticalities of several three-dimensional (3D) models on the cubic lattice, including the classical O(3)O(3)O(3) model, the 5-state ferromagnetic Potts model, and a dimerized quantum antiferromagnetic Heisenberg model. Particularly, although the considered NN is only trained one time on a one-dimensional (1D) lattice with 120 sites, yet it has successfully determined the related critical points of the studied 3D systems. Moreover, real configurations of states are not used in the testing stage. Instead, the employed configurations for the prediction are constructed on a 1D lattice of 120 sites and are based on the bulk quantities or the microscopic states of the considered models. As a result, our calculations are ultimately efficient in computation and the applications of the built NN is extremely broaden. Considering the fact that the investigated systems vary dramatically from each other, it is amazing that the combination of these two strategies in the training and the testing stages lead to a highly universal supervised neural network for learning phases and criticalities of 3D models. Based on the outcomes presented in this study, it is favorably probable that much simpler but yet elegant machine learning techniques can be constructed for fields of many-body systems other than the critical phenomena.
Berezinskii--Kosterlitz--Thouless transition of the two-dimensional XYXYXY model on the honeycomb lattice
The Berezinskii--Kosterlitz--Thouless (BKT) transition of the two-dimensional XYXYXY 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 TBKT,HT_{\text{BKT,H}}TBKT,H​ is found to be 12\frac{1}{\sqrt{2}}2​1​ exactly. Surprisingly, the value of TBKT,HT_{\text{BKT,H}}TBKT,H​ obtained from our NN calculations is 0.560(9) which deviates significantly from 12\frac{1}{\sqrt{2}}2​1​. In addition, based on the helicity modulus, the TBKT,HT_{\text{BKT,H}}TBKT,H​ determined is 0.571(8) agreeing well with that resulting from the NN estimation. The outcomes presented in this study indicate that a detailed analytic calculation is desirable to solve the found discrepancy.
We study the phase transitions of three-dimensional (3D) classical O(3)O(3)O(3) model and two-dimensional (2D) classical XY model, as well as both the quantum phase transitions of 2D and 3D dimerized spin-1/2 antiferromagnets, using the technique of supervised neural network (NN). Moreover, unlike the conventional approaches commonly used in the literature, the training sets employed in our investigation are neither the theoretical nor the real configurations of the considered systems. Remarkably, with such an unconventional set up of the training stage in conjunction with some semiexperimental finite-size scaling formulas, the associated critical points determined by the NN method agree well with the established results in the literature. The outcomes obtained here imply that certain unconventional training strategies, like the one used in this study, are not only cost-effective in computation but are also applicable for a wide range of physical systems.
A universal (supervised) neural network (NN), which is only trained once on a one-dimensional lattice of 200 sites, is employed to study the phase transition of the two-dimensional (2D) 5-state ferromagnetic Potts model on the square lattice. In particular, the NN is obtained by using merely two artificially made configurations as the training set. Due to the elegant features of the considered NN, results associated with systems consisting of over 4000000 spins can be obtained with ease, and convincing evidence showing the investigated phase transition is weakly first order is reached. The outcomes demonstrated here can hardly be achieved with the standard NNs that are commonly used in the literature.