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

Journal of Physics Conference Series

Monte Carlo simulation with Wolff algorithm for scaling behavior of two dimensional XY model with KT phase transition

Yuntai Song

Published Nov 1, 2023• 0 citations
Publisher

Abstract

Abstract The property of XY model with its KT phase transition has been discussed in many aspects such as specific heat and magnetic susceptibility along with correlation function. Also, this is one of the original models for topological phase transition which gives a new type of phase transition without symmetry breaking. Since the calculation of these properties above can be achieved by Monte Carlo Method with Wolff algorithm, the visualization of vortex and antivortex is also an interesting task which is accomplished in this article. By successfully modeling the system and getting the step-by-step configuration, the relation between the generation of vortex and the variation of temperature can be concluded in a qualitative way. The calculation of spin correlation function shows the phase transition between disorder and quasi long-range order which represents the topological phase transition. As a reliable method, the Monte Carlo method with Wolff algorithm can be a choice of generating the training set for neural network which can calculated much more sophisticated case in a relatively short time and the transition between classical simulation and quantum simulation can be approached as mentioned in the end of this article.

DOI
10.1088/1742-6596/2649/1/012055

Related papers

Phase transitions in the two-dimensional XY model with random phases: A Monte Carlo study

J. Maucourt, Daniel R. Grempel

We study the two-dimensional $\mathrm{XY}$ model with quenched random phases by Monte Carlo simulation and finite-size scaling analysis. We determine the phase diagram of the model and study its critical behavior as a function of disorder and temperature. If the strength of the randomness is less than a critical value, ${\ensuremath{\sigma}}_{c},$ the system has a Kosterlitz-Thouless (KT) phase transition from the paramagnetic phase to a state with quasi-long-range order. Our data suggest that the latter exists down to $T=0$ in contradiction with theories that predict the appearance of a low-temperature reentrant phase. At the critical disorder ${T}_{\mathrm{KT}}\ensuremath{\rightarrow}0$ and for $\ensuremath{\sigma}>{\ensuremath{\sigma}}_{c}$ there is no quasiordered phase. At zero temperature there is a phase transition between two different glassy states at ${\ensuremath{\sigma}}_{c}.$ The functional dependence of the correlation length on $\ensuremath{\sigma}$ suggests that this transition corresponds to the disorder-driven unbinding of vortex pairs.

arXiv:cond-mat/9703109•Physical review. B, Condensed matter•Aug 1, 1997•30 citations

Simulation of Kosterlitz-Thouless (KT) Transition with Classical Monte-Carlo Simulation

Nepal Banerjee

Spontaneous symmetry breaking of 2D isotropic Heisenberg magnet is restricted by Mermin-Wagner theorem at any finite temperature in presence of short-range exchange interaction.Kosterlitz and Thouless using XY spin model showed that how an order state could developed in 2D spin system in presence of short range isotropic interaction.Very recent discovery of several van der waals magnet revised and redefined our understanding on 2D Heisenberg magnet and its ground state properties.After a rigorous and careful study of several 2D magnetic material we have realized from both experimentally and numerically that the finite size of a 2D system has great impact on the ground state symmetry breaking.Because of that finite size effect more often an anisotropic residual magnetic moment is generated and trigger the spontaneous symmetry breaking at finite temperature(T) and even only presence of short-range interaction we observed the phase transition of that Heisenberg spin system.In this present work we have shown the basic role of finite size,anisotropy during the symmetry breaking of 2D Heisenberg XY magnet.Here we have simulated Kosterlitz-Thouless transition using classical Monte-carlo simulation and study the effect of anisotropy during the phase transition.We presented the behaviour of different thermodynamic properties of 2D XY spin model system during the Kosterlitz-Thouless(KT) transition.The generic characteristic of KT transition which make it distinct from other critical phenomena is that the peak of heat capacity is not diverging with increase of system size rather peak is decreasing with the increasing of system size near at transition temperature.Here we are observing that behaviour in our present simulation and that specific behaviour help us for classifying the present transition as Kosterlitz-Thouless(KT) transition.

arXiv:2307.10310•Jul 19, 2023•0 citations

MONTE CARLO STUDY OF TIIE TWO-DIMENSIONAL SPIN-I/2 XY MODEL ~

Hans A. De Raedt, Bart De Raedt

The generalized Trotter formula is used to map the two-dimensional spin-l/2 XY model onto a three-dimensional lsing model with complicated many-spin interactions. This relationship sused to construct an efficient Monte Carlo algorithm. Simulation data for the specific heat and vortex correlation functions give strong evidence for the existence of a phase transition. Although it is well known that there cannot exist long-range order in the two-dimensional (2D) spin-1/2 XY model at non-zero temperature [1], high-temper-ature series expansions [2] suggest he existence of critical behavior. Little is known about the quantum model mainly because most techniques which have been succesfully applied to the classical model (also referred to as planar rotator model) are very difficult to extend to the quantum case. In particular, quantum renormalization group analYsis of the 2D spin-1/2 XY model have given either contradictive or unreliable re-suits [3-8]. An alternative method to calculate the thermody-namic properties of this modelis to exploit the formal analogy between d-dimensional quantum spin systems and (d + 1)-dimensional Ising-spin models [9]. Using ~ ' This paper was first submitted to Physical Review Letters

•Jan 1, 1983•0 citations

Finite size scaling and first-order phase transition in a modified XY model

Suman Sinha, Soumen Roy

Monte Carlo simulation has been performed in a two-dimensional modified XY -model first proposed by Domany [Phys. Rev. Lett. 52, 1535 (1984)] The cluster algorithm of Wolff has been used and multiple histogram reweighting is performed. The first-order scaling behavior of the quantities such as specific heat and free-energy barrier are found to be obeyed accurately. While the lowest-order correlation function was found to decay to zero at long distance just above the transition, the next-higher-order correlation function shows a nonzero plateau.

arXiv:0907.4243•Physical Review E•Feb 16, 2010•16 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.

arXiv:2406.12076•Physica Scripta•May 8, 2025•3 citations

Emergent topological ordered phase for the Ising-XY model revealed by cluster-updating Monte Carlo method

Heyang Ma, Wanzhou 万舟 Zhang 张, Yanting 彦婷 Tian 田 +2 more

The two-component cold atom systems with anisotropic hopping amplitudes can be phenomenologically described by a two-dimensional Ising-XY coupled model with spatial anisotropy. At low temperatures, theoretical predictions [Phys. Rev. A 72 053604 (2005)] and [arXiv: 0706.1609] indicate the existence of a topological ordered phase characterized by Ising and XY disorder but with 2XY ordering. However, due to ergodic difficulties faced by Monte Carlo methods at low temperatures, this topological phase has not been numerically explored. We propose a linear cluster updating Monte Carlo method, which flips spins without rejection in the anisotropy limit but does not change the energy. Using this scheme and conventional Monte Carlo methods, we succeed in revealing the nature of topological phases with half-vortices and domain walls. In the constructed global phase diagram, Ising and XY-type transitions are very close to each other and differ significantly from the schematic phase diagram reported earlier. We also propose and explore a wide range of quantities, including magnetism, superfluidity, specific heat, susceptibility, and even percolation susceptibility, and obtain consistent and reliable results. Furthermore, we observed first-order transitions characterized by common intersection points in magnetizations for different system sizes, as opposed to the conventional phase transition where Binder cumulants of various sizes share common intersections. The critical exponents of different types of phase transitions are reasonably fitted. The results are useful to help cold atom experiments explore the half-vortex topological phase.

arXiv:2310.20314•Chinese Physics B•Jan 11, 2024•4 citations
Abstract The property of XY model with its KT phase transition has been discussed in many aspects such as specific heat and magnetic susceptibility along with correlation function. Also, this is one of the original models for topological phase transition which gives a new type of phase transition without symmetry breaking. Since the calculation of these properties above can be achieved by Monte Carlo Method with Wolff algorithm, the visualization of vortex and antivortex is also an interesting task which is accomplished in this article. By successfully modeling the system and getting the step-by-step configuration, the relation between the generation of vortex and the variation of temperature can be concluded in a qualitative way. The calculation of spin correlation function shows the phase transition between disorder and quasi long-range order which represents the topological phase transition. As a reliable method, the Monte Carlo method with Wolff algorithm can be a choice of generating the training set for neural network which can calculated much more sophisticated case in a relatively short time and the transition between classical simulation and quantum simulation can be approached as mentioned in the end of this article.
We study the two-dimensional XY\mathrm{XY}XY model with quenched random phases by Monte Carlo simulation and finite-size scaling analysis. We determine the phase diagram of the model and study its critical behavior as a function of disorder and temperature. If the strength of the randomness is less than a critical value, ${\ensuremath{\sigma}}_{c},$ the system has a Kosterlitz-Thouless (KT) phase transition from the paramagnetic phase to a state with quasi-long-range order. Our data suggest that the latter exists down to T=0T=0T=0 in contradiction with theories that predict the appearance of a low-temperature reentrant phase. At the critical disorder ${T}_{\mathrm{KT}}\ensuremath{\rightarrow}0$ and for $\ensuremath{\sigma}>{\ensuremath{\sigma}}_{c}$ there is no quasiordered phase. At zero temperature there is a phase transition between two different glassy states at ${\ensuremath{\sigma}}_{c}.$ The functional dependence of the correlation length on $\ensuremath{\sigma}$ suggests that this transition corresponds to the disorder-driven unbinding of vortex pairs.
Spontaneous symmetry breaking of 2D isotropic Heisenberg magnet is restricted by Mermin-Wagner theorem at any finite temperature in presence of short-range exchange interaction.Kosterlitz and Thouless using XY spin model showed that how an order state could developed in 2D spin system in presence of short range isotropic interaction.Very recent discovery of several van der waals magnet revised and redefined our understanding on 2D Heisenberg magnet and its ground state properties.After a rigorous and careful study of several 2D magnetic material we have realized from both experimentally and numerically that the finite size of a 2D system has great impact on the ground state symmetry breaking.Because of that finite size effect more often an anisotropic residual magnetic moment is generated and trigger the spontaneous symmetry breaking at finite temperature(T) and even only presence of short-range interaction we observed the phase transition of that Heisenberg spin system.In this present work we have shown the basic role of finite size,anisotropy during the symmetry breaking of 2D Heisenberg XY magnet.Here we have simulated Kosterlitz-Thouless transition using classical Monte-carlo simulation and study the effect of anisotropy during the phase transition.We presented the behaviour of different thermodynamic properties of 2D XY spin model system during the Kosterlitz-Thouless(KT) transition.The generic characteristic of KT transition which make it distinct from other critical phenomena is that the peak of heat capacity is not diverging with increase of system size rather peak is decreasing with the increasing of system size near at transition temperature.Here we are observing that behaviour in our present simulation and that specific behaviour help us for classifying the present transition as Kosterlitz-Thouless(KT) transition.
The generalized Trotter formula is used to map the two-dimensional spin-l/2 XY model onto a three-dimensional lsing model with complicated many-spin interactions. This relationship sused to construct an efficient Monte Carlo algorithm. Simulation data for the specific heat and vortex correlation functions give strong evidence for the existence of a phase transition. Although it is well known that there cannot exist long-range order in the two-dimensional (2D) spin-1/2 XY model at non-zero temperature [1], high-temper-ature series expansions [2] suggest he existence of critical behavior. Little is known about the quantum model mainly because most techniques which have been succesfully applied to the classical model (also referred to as planar rotator model) are very difficult to extend to the quantum case. In particular, quantum renormalization group analYsis of the 2D spin-1/2 XY model have given either contradictive or unreliable re-suits [3-8]. An alternative method to calculate the thermody-namic properties of this modelis to exploit the formal analogy between d-dimensional quantum spin systems and (d + 1)-dimensional Ising-spin models [9]. Using ~ ' This paper was first submitted to Physical Review Letters
Monte Carlo simulation has been performed in a two-dimensional modified XY -model first proposed by Domany [Phys. Rev. Lett. 52, 1535 (1984)] The cluster algorithm of Wolff has been used and multiple histogram reweighting is performed. The first-order scaling behavior of the quantities such as specific heat and free-energy barrier are found to be obeyed accurately. While the lowest-order correlation function was found to decay to zero at long distance just above the transition, the next-higher-order correlation function shows a nonzero plateau.
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.
The two-component cold atom systems with anisotropic hopping amplitudes can be phenomenologically described by a two-dimensional Ising-XY coupled model with spatial anisotropy. At low temperatures, theoretical predictions [Phys. Rev. A 72 053604 (2005)] and [arXiv: 0706.1609] indicate the existence of a topological ordered phase characterized by Ising and XY disorder but with 2XY ordering. However, due to ergodic difficulties faced by Monte Carlo methods at low temperatures, this topological phase has not been numerically explored. We propose a linear cluster updating Monte Carlo method, which flips spins without rejection in the anisotropy limit but does not change the energy. Using this scheme and conventional Monte Carlo methods, we succeed in revealing the nature of topological phases with half-vortices and domain walls. In the constructed global phase diagram, Ising and XY-type transitions are very close to each other and differ significantly from the schematic phase diagram reported earlier. We also propose and explore a wide range of quantities, including magnetism, superfluidity, specific heat, susceptibility, and even percolation susceptibility, and obtain consistent and reliable results. Furthermore, we observed first-order transitions characterized by common intersection points in magnetizations for different system sizes, as opposed to the conventional phase transition where Binder cumulants of various sizes share common intersections. The critical exponents of different types of phase transitions are reasonably fitted. The results are useful to help cold atom experiments explore the half-vortex topological phase.