arXiv:2004.06314 · Journal of Statistical Mechanics Theory and Experiment

Critical analysis of two-dimensional classical XY model

Raghav G Jha

Published Aug 1, 2020• 22 citations

Abstract

Abstract We consider the two-dimensional classical XY model on a square lattice in the thermodynamic limit using tensor renormalization group and precisely determine the critical temperature corresponding to the Berezinskii–Kosterlitz–Thouless (BKT) phase transition to be 0.89290(5) which is an improvement compared to earlier studies using tensor network methods.

DOI: 10.1088/1742-5468/aba686

Related papers

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

Fu-Jiun Jiang

Progress of Theoretical and Experimental PhysicsSep 26, 20244 citations

Berezinskii-Kosterlitz-Thouless transition in the XY model on the honeycomb lattice: a comprehensive Monte Carlo analysis

Felipe E. F. de Andrade, L. N. Jorge, Cláudio José DaSilva

arXiv:2406.12076Physica ScriptaMay 8, 20253 citations

Critical properties of the two-dimensional q -state clock model

Zi-Qian Li, Li‐Ping Yang, Z. Y. Xie +3 more

arXiv:1912.11416Physical review. EJun 24, 202072 citations

Tensor renormalization group study of classical XY model on the square lattice

Ji-Feng Yu, Z. Y. Xie, Yannick Meurice +6 more

arXiv:1309.4963Physical Review EJan 22, 201496 citations

Resolving the Berezinskii-Kosterlitz-Thouless transition in the two-dimensional XY model with tensor-network-based level spectroscopy

Atsushi Ueda, Masaki Oshikawa

arXiv:2105.11460Physical review. B./Physical review. BOct 20, 202126 citations

Phase diagram of generalized XY model using the tensor renormalization group

Abhishek Samlodia, Vamika Longia, Raghav G. Jha +1 more

arXiv:2404.17504Physical review. D/Physical review. D.Aug 6, 202411 citations

arXiv:2004.06314 · Journal of Statistical Mechanics Theory and Experiment

Critical analysis of two-dimensional classical XY model

Raghav G Jha

Published Aug 1, 2020• 22 citations

arXiv HTML PDF

Abstract

DOI: 10.1088/1742-5468/aba686

Related papers

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.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 PhysicsSep 26, 20244 citations

Berezinskii-Kosterlitz-Thouless transition in the XY model on the honeycomb lattice: a comprehensive Monte Carlo analysis

Felipe E. F. de Andrade, L. N. Jorge, Cláudio José DaSilva

Abstract In this paper, we thoroughly examined the Berezinskii-Kosterlitz-Thouless (BKT) phase transition in the two-dimensional XY model on the honeycomb lattice. To address its thermodynamical behavior, we combined standard numerical Monte Carlo simulations with the simulated annealing (SA) protocol and entropic simulations based on the Wang-Landau (WL) algorithm. The transition temperature was determined using the second (ϒ) and fourth-order (ϒ4) helicity modulus as the order parameter. Our best finite-size scaling analysis suggests T BKT = 0.575(8) from SA and T BKT = 0.576(3) from WL. These values deviate significantly from the expected theoretical value of 1 / 2 . We believe that this discrepancy suggests that the theoretical assumptions regarding the analytical calculation may need to be revisited. Additionally, we calculated the vortex density and the formation energy of the vortex-antivortex pairs, where the obtained vortex formation energy is 2μ = 5.80(12). Upon comparison with the square lattice, our results support the notion of instability of the honeycomb lattice to support the spin long-range order and give additional backing to the critical behavior we found.Abstract In this paper, we thoroughly examined the Berezinskii-Kosterlitz-Thouless (BKT) phase transition in the two-dimensional XY model on the honeycomb lattice. To address its thermodynamical behavior, we combined standard numerical Monte Carlo simulations with the simulated annealing (SA) protocol and entropic simulations based on the Wang-Landau (WL) algorithm. The transition temperature was determined using the second (ϒ) and fourth-order (ϒ4) helicity modulus as the order parameter. Our best finite-size scaling analysis suggests T BKT = 0.575(8) from SA and T BKT = 0.576(3) from WL. These values deviate significantly from the expected theoretical value of 1 / 2 . We believe that this discrepancy suggests that the theoretical assumptions regarding the analytical calculation may need to be revisited. Additionally, we calculated the vortex density and the formation energy of the vortex-antivortex pairs, where the obtained vortex formation energy is 2μ = 5.80(12). Upon comparison with the square lattice, our results support the notion of instability of the honeycomb lattice to support the spin long-range order and give additional backing to the critical behavior we found.

arXiv:2406.12076Physica ScriptaMay 8, 20253 citations

Critical properties of the two-dimensional q -state clock model

Zi-Qian Li, Li‐Ping Yang, Z. Y. Xie +3 more

We perform the state-of-the-art tensor network simulations directly in the thermodynamic limit to clarify the critical properties of the q-state clock model on the square lattice. We determine accurately the two phase transition temperatures through the singularity of the classical analog of the entanglement entropy, and provide extensive numerical evidences to show that both transitions are of the Berezinskii-Kosterlitz-Thouless (BKT) type for q≥5 and that the low-energy physics of this model is well described by the Z_{q}-deformed sine-Gordon theory. We also determine the characteristic conformal parameters, especially the compactification radius, that govern the critical properties of the intermediate BKT phase.We perform the state-of-the-art tensor network simulations directly in the thermodynamic limit to clarify the critical properties of the q-state clock model on the square lattice. We determine accurately the two phase transition temperatures through the singularity of the classical analog of the entanglement entropy, and provide extensive numerical evidences to show that both transitions are of the Berezinskii-Kosterlitz-Thouless (BKT) type for q≥5 and that the low-energy physics of this model is well described by the Z_{q}-deformed sine-Gordon theory. We also determine the characteristic conformal parameters, especially the compactification radius, that govern the critical properties of the intermediate BKT phase.

arXiv:1912.11416Physical review. EJun 24, 202072 citations

Tensor renormalization group study of classical XY model on the square lattice

Ji-Feng Yu, Z. Y. Xie, Yannick Meurice +6 more

Using the tensor renormalization group method based on the higher-order singular value decomposition, we have studied the thermodynamic properties of the continuous XY model on the square lattice. The temperature dependence of the free energy, the internal energy, and the specific heat agree with the Monte Carlo calculations. From the field dependence of the magnetic susceptibility, we find the Kosterlitz-Thouless transition temperature to be 0.8921(19), consistent with the Monte Carlo as well as the high temperature series expansion results. At the transition temperature, the critical exponent δ is estimated as 14.5, close to the analytic value by Kosterlitz.Using the tensor renormalization group method based on the higher-order singular value decomposition, we have studied the thermodynamic properties of the continuous XY model on the square lattice. The temperature dependence of the free energy, the internal energy, and the specific heat agree with the Monte Carlo calculations. From the field dependence of the magnetic susceptibility, we find the Kosterlitz-Thouless transition temperature to be 0.8921(19), consistent with the Monte Carlo as well as the high temperature series expansion results. At the transition temperature, the critical exponent δ is estimated as 14.5, close to the analytic value by Kosterlitz.

arXiv:1309.4963Physical Review EJan 22, 201496 citations

Resolving the Berezinskii-Kosterlitz-Thouless transition in the two-dimensional XY model with tensor-network-based level spectroscopy

Atsushi Ueda, Masaki Oshikawa

Berezinskii-Kosterlitz-Thouless transition of the classical XY model is reinvestigated, combining the tensor network renormalization (TNR) and the level spectroscopy method based on the finite-size scaling of the conformal field theory. By systematically analyzing the spectrum of the transfer matrix of the systems of various moderate sizes, which can be accurately handled with a finite bond dimension, we determine the critical point removing the logarithmic corrections. This improves the accuracy by an order of magnitude over previous studies including those utilizing TNR. Our analysis also gives a visualization of the celebrated Kosterlitz renormalization group flow based on the numerical data.Berezinskii-Kosterlitz-Thouless transition of the classical XY model is reinvestigated, combining the tensor network renormalization (TNR) and the level spectroscopy method based on the finite-size scaling of the conformal field theory. By systematically analyzing the spectrum of the transfer matrix of the systems of various moderate sizes, which can be accurately handled with a finite bond dimension, we determine the critical point removing the logarithmic corrections. This improves the accuracy by an order of magnitude over previous studies including those utilizing TNR. Our analysis also gives a visualization of the celebrated Kosterlitz renormalization group flow based on the numerical data.

arXiv:2105.11460Physical review. B./Physical review. BOct 20, 202126 citations

Phase diagram of generalized XY model using the tensor renormalization group

Abhishek Samlodia, Vamika Longia, Raghav G. Jha +1 more

We use the higher-order tensor renormalization group method to study the two-dimensional generalized XY model that admits integer and half-integer vortices. This model is the deformation of the classical XY model and has a rich phase structure consisting of nematic, ferromagnetic, and disordered phases and three transition lines belonging to the Berezinskii-Kosterlitz-Thouless and Ising class. We explore the model for a wide range of temperatures, T , and the deformation parameter, Δ , and compute specific heat along with integer and half-integer magnetic susceptibility, finding both Berezinskii-Kosterlitz-Thouless-like and Ising-like transitions and the region where they meet. Published by the American Physical Society 2024We use the higher-order tensor renormalization group method to study the two-dimensional generalized XY model that admits integer and half-integer vortices. This model is the deformation of the classical XY model and has a rich phase structure consisting of nematic, ferromagnetic, and disordered phases and three transition lines belonging to the Berezinskii-Kosterlitz-Thouless and Ising class. We explore the model for a wide range of temperatures, T , and the deformation parameter, Δ , and compute specific heat along with integer and half-integer magnetic susceptibility, finding both Berezinskii-Kosterlitz-Thouless-like and Ising-like transitions and the region where they meet. Published by the American Physical Society 2024

arXiv:2404.17504Physical review. D/Physical review. D.Aug 6, 202411 citations

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.