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

arXiv:cond-mat/9702081 · Physical review. B, Condensed matter

Universal jump in the helicity modulus of the two-dimensional quantum XY model

Kenji Harada, Naoki Kawashima

Published May 1, 1997• 78 citations
arXivHTMLPDF

Abstract

The helicity modulus of the S=1/2 XY model is precisely estimated through a world-line quantum Monte Carlo method enhanced by a cluster update algorithm. The obtained estimates for various system sizes and temperatures are well fitted by a scaling form with L replaced by log (L/${\mathrm{L}}_{0}$), which is inferred from the solution of the Kosterlitz renormalization group equation. The validity of the Kosterlitz-Thouless theory for this model is confirmed.

DOI
10.1103/physrevb.55.r11949

Related papers

Kosterlitz-Thouless Transition of QuantumXYModel in Two Dimensions

Kenji Harada, Naoki Kawashima

The two-dimensional $S=1/2$ XY model is investigated with an extensive quantum Monte Carlo simulation. The helicity modulus is precisely estimated through a continuous-time loop algorithm for systems up to $128 \times 128$ near and below the critical temperature. The critical temperature is estimated as $T_{\rm KT} = 0.3427(2)J$. The obtained estimates for the helicity modulus are well fitted by a scaling form derived from the Kosterlitz renormalization group equation. The validity of the Kosterlitz-Thouless theory for this model is confirmed.

arXiv:cond-mat/9803090•Journal of the Physical Society of Japan•Aug 15, 1998•79 citations

The two-dimensional XY model at the transition temperature: a high-precision Monte Carlo study

Martin Hasenbusch

We study the classical XY (plane rotator) model at the Kosterlitz–Thouless phase transition. We simulate the model using the single-cluster algorithm on square lattices of a linear size up to L = 2048. We derive the finite-size behaviour of the second moment correlation length over the lattice size ξ 2nd / L at the transition temperature. This new prediction and the analogous one for the helicity modulus ϒ are confronted with our Monte Carlo data. This way β KT = 1.1199 is confirmed as inverse transition temperature. Finally, we address the puzzle of logarithmic corrections of the magnetic susceptibility χ at the transition temperature.

arXiv:cond-mat/0502556•Journal of Physics A Mathematical and General•Jun 15, 2005•165 citations

Large-Scale Monte Carlo Simulation of Two-Dimensional Classical XY Model Using Multiple GPUs

Yukihiro Komura, Yutaka Okabe

We study the two-dimensional classical XY model by the large-scale Monte Carlo simulation of the Swendsen-Wang multi-cluster algorithm using multiple GPUs on the open science supercomputer TSUBAME 2.0. Simulating systems up to the linear system size L=65536, we investigate the Kosterlitz-Thouless (KT) transition. Using the generalized version of the probability-changing cluster algorithm based on the helicity modulus, we locate the KT transition temperature in a self-adapted way. The obtained inverse KT temperature β_{KT} is 1.11996(6). We estimate the exponent to specify the multiplicative logarithmic correction, -2r, and precisely reproduce the theoretical prediction -2r=1/8.

arXiv:1210.6116•Journal of the Physical Society of Japan•Oct 12, 2012•80 citations

Monte Carlo analysis of the two-dimensionalXYmodel. II. Comparison with the Kosterlitz renormalization-group equations

Peter Olsson

The temperature scale of relevance for the vortex excitations in the two-dimensional XY model is identified. The size dependence of the helicity modulus at constant vortex temperature is then obtained by Monte Carlo simulations. The Monte Carlo data are then compared with the results for the length-dependent dielectric function from the Kosterlitz renormalization-group equations. The agreement is excellent for temperatures up to and slightly above ${\mathit{T}}_{\mathit{c}}$. The critical temperature is determined to be ${\mathit{T}}_{\mathit{c}}$=0.892 13(10). The temperature dependence of the characteristic length right above ${\mathit{T}}_{\mathit{c}}$ is also obtained and found to be in agreement with recent results from high-temperature series expansions.

Physical review. B, Condensed matter•Aug 1, 1995•110 citations

On the helicity modulus, the critical temperature and Monte Carlo simulations for the two-dimensional XY-model

Peter Olsson, Petter Minnhagen

A lattice size dependence of the helicity modulus for the two-dimensional XY-model is inferred by aid of the Coulomb gas-vortex analogy and an explicit form of this dependence is obtained from a set of self-consistent equations for the Coulomb gas. High precision Monte Carlo simulations in conjunction with this inferred lattice size dependence is used to determine the critical temperature. Some other recent results in the literature are discussed in the light of the present investigation.

Physica Scripta•Feb 1, 1991•38 citations

Finite-size scaling of the helicity modulus of the two-dimensional O(3) model

Norbert Schultka

Using Monte Carlo methods, we compute the finite-size scaling function of the helicity modulus \ensuremath{\Upsilon} of the two-dimensional O(3) model and compare it to the low-temperature expansion prediction. From this, we estimate the range of validity for the leading terms of the low-temperature expansion of the finite-size scaling function and for the low-temperature expansion of the correlation length. Our results strongly suggest that a Kosterlitz-Thouless transition at a temperature T>0 is extremely unlikely in this model.

arXiv:cond-mat/9611043•Physical review. B, Condensed matter•Jan 1, 1997•3 citations
The helicity modulus of the S=1/2 XY model is precisely estimated through a world-line quantum Monte Carlo method enhanced by a cluster update algorithm. The obtained estimates for various system sizes and temperatures are well fitted by a scaling form with L replaced by log (L/L0{\mathrm{L}}_{0}L0​), which is inferred from the solution of the Kosterlitz renormalization group equation. The validity of the Kosterlitz-Thouless theory for this model is confirmed.
The two-dimensional S=1/2S=1/2S=1/2 XY model is investigated with an extensive quantum Monte Carlo simulation. The helicity modulus is precisely estimated through a continuous-time loop algorithm for systems up to 128×128128 \times 128128×128 near and below the critical temperature. The critical temperature is estimated as TKT=0.3427(2)JT_{\rm KT} = 0.3427(2)JTKT​=0.3427(2)J. The obtained estimates for the helicity modulus are well fitted by a scaling form derived from the Kosterlitz renormalization group equation. The validity of the Kosterlitz-Thouless theory for this model is confirmed.
We study the classical XY (plane rotator) model at the Kosterlitz–Thouless phase transition. We simulate the model using the single-cluster algorithm on square lattices of a linear size up to L = 2048. We derive the finite-size behaviour of the second moment correlation length over the lattice size ξ 2nd / L at the transition temperature. This new prediction and the analogous one for the helicity modulus ϒ are confronted with our Monte Carlo data. This way β KT = 1.1199 is confirmed as inverse transition temperature. Finally, we address the puzzle of logarithmic corrections of the magnetic susceptibility χ at the transition temperature.
We study the two-dimensional classical XY model by the large-scale Monte Carlo simulation of the Swendsen-Wang multi-cluster algorithm using multiple GPUs on the open science supercomputer TSUBAME 2.0. Simulating systems up to the linear system size L=65536, we investigate the Kosterlitz-Thouless (KT) transition. Using the generalized version of the probability-changing cluster algorithm based on the helicity modulus, we locate the KT transition temperature in a self-adapted way. The obtained inverse KT temperature β_{KT} is 1.11996(6). We estimate the exponent to specify the multiplicative logarithmic correction, -2r, and precisely reproduce the theoretical prediction -2r=1/8.
The temperature scale of relevance for the vortex excitations in the two-dimensional XY model is identified. The size dependence of the helicity modulus at constant vortex temperature is then obtained by Monte Carlo simulations. The Monte Carlo data are then compared with the results for the length-dependent dielectric function from the Kosterlitz renormalization-group equations. The agreement is excellent for temperatures up to and slightly above Tc{\mathit{T}}_{\mathit{c}}Tc​. The critical temperature is determined to be Tc{\mathit{T}}_{\mathit{c}}Tc​=0.892 13(10). The temperature dependence of the characteristic length right above Tc{\mathit{T}}_{\mathit{c}}Tc​ is also obtained and found to be in agreement with recent results from high-temperature series expansions.
Using Monte Carlo methods, we compute the finite-size scaling function of the helicity modulus \ensuremath{\Upsilon} of the two-dimensional O(3) model and compare it to the low-temperature expansion prediction. From this, we estimate the range of validity for the leading terms of the low-temperature expansion of the finite-size scaling function and for the low-temperature expansion of the correlation length. Our results strongly suggest that a Kosterlitz-Thouless transition at a temperature T>0 is extremely unlikely in this model.