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 A Mathematical and Theoretical

On the topological phase transition of the two-dimensional XY-model on the Voronoi–Delaunay lattice

Nemesio Matos Oliveira-Neto, Sidiney G. Alves, R. L. Silva, A. R. Pereira, W. A. Moura-Melo

Published Sep 1, 2009• 2 citations
Publisher

Abstract

We numerically investigate the static properties of the two-dimensional (2D) XY-model on the Voronoi–Delaunay lattice, with average connectivity . The critical temperature, magnetization and vortex density are obtained. For instance, in this lattice the critical temperature, above which free vortices take place, reads TVDcr ≈ 1.22 (in units of J, the exchange constant), higher than their counterparts for regular square, TSLcr ≈ 0.79, and triangular lattices TTLcr ≈ 1.156, with constant connectivity given by 4 and 6, respectively. Such results lead us to argue that not only the connectivity number but also how the sites are distributed and linked among themselves is also important for determining these physical quantities.

DOI
10.1088/1751-8113/42/38/385002

Related papers

Critical behavior of the spin-1 Blume-Capel model on two-dimensional Voronoi-Delaunay random lattices

Francivaldo Pinheiro Fernandes, Douglas F. de Albuquerque, F. W. S. Lima +1 more

The critical properties of the spin-1 Blume-Capel model in two dimensions is studied on Voronoi-Delaunay random lattices with quenched connectivity disorder. The system is treated by applying Monte Carlo simulations using the heat-bath update algorithm together with single histograms re-weighting techniques. We calculate the critical temperature as well as the critical exponents as a function of the crystal field $\mathrm{\ensuremath{\Delta}}$. It is found that this disordered system exhibits phase transitions of first- and second-order types that depend on the value of the crystal field. For values of $\mathrm{\ensuremath{\Delta}}\ensuremath{\le}3$, where the nearest-neighbor exchange interaction $J$ has been set to unity, the disordered system presents a second-order phase transition. The results suggest that the corresponding exponent ratio belongs to the same universality class as the regular two-dimensional ferromagnetic model. There exists a tricritical point close to ${\mathrm{\ensuremath{\Delta}}}_{t}=3.05(4)$ with different critical exponents. For ${\mathrm{\ensuremath{\Delta}}}_{t}\ensuremath{\le}\mathrm{\ensuremath{\Delta}}<3.4$ this model undergoes a first-order phase transition. Finally, for $\mathrm{\ensuremath{\Delta}}\ensuremath{\ge}3.4$ the system is always in the paramagnetic phase.

Physical Review E•Aug 26, 2015•9 citations

Critical behavior of the fully frustrated two dimensional XY model

Anderson Barbosa Lima, B. V. Costa

Using Monte Carlo simulations we have investigated the critical behavior of the classical fully frustrated XY model in two dimensions in a square lattice. There are two phase transitions in the model, one of the Berezinskii-Kosterlitz-Thouless type and a Z2 transition at higher temperature. We show that the vortex anti-vortex density has a clear signature of the Z2 phase transition at exactly the percolation threshold.

Brazilian Journal of Physics•Jun 1, 2004•3 citations

Numerical Studies of Vortices and Helicity Modulus in the Two-Dimensional Generalized XY Model

Yunzhou Sun, Qin Wu, Yang Xiao-li +4 more

Two-dimensional generalized XY spin model on a triangular lattice is studied by means of Monte-Carlo simulations. The critical temperatures of Berezinskii-Kosterlitz-Thouless (BKT) phase transition are obtained by the method of helicity modulus. It is found that the results are consistent with those obtained by other methods. The vortex density and the vortex-antivortex pair formation energy are also obtained. The result shows that the critical temperature decreases with the increase of the generalization parameter q . While the vortex-antivortex pair formation energy increases with the increase of q when q>1 .

Frontiers in Physics•Mar 4, 2022•3 citations

Phase transitions in two-dimensional antiferromagnetic XY models in external field

Виктор Степанович Доценко, G. Uimin

A qualitative study has been performed to elucidate the critical properties of an antiferromagnetic planar system in two dimensions. Phase diagrams in the temperature-field plane differ considerably in the cases of square and triangular lattices, resulting in the latter case in coexistence of the Ising-type and vortex unbinding phase transitions.

Journal of Physics C Solid State Physics•Sep 10, 1985•11 citations

Single-cluster Monte Carlo study of the Ising model on two-dimensional random lattices

Wolfhard Janke E, Mohammad W. Katoot, Ramon Villanova

We use the single-cluster Monte Carlo update algorithm to simulate the Ising model on two-dimensional Poissonian random lattices with up to 80 000 sites which are linked together according to the Voronoi-Delaunay prescription. In one set of simulations we use reweighting techniques and finite-size scaling analysis to investigate the critical properties of the model in the very vicinity of the phase transition. In the other set of simulations we study the approach to criticality in the disordered phase, making use of improved estimators for measurements. From both sets of simulations we obtain clear evidence that the critical exponents agree with the exactly known exponents for regular lattices, i.e., that (lattice) universality holds for the two-dimensional Ising model.

arXiv:hep-lat/9402008•Physical review. B, Condensed matter•Apr 1, 1994•60 citations

Topological Lattice Actions for the 2d XY Model

Wolfgang Bietenholz A, Bögli, Michael, Niedermayer, Ferenc +3 more

We consider the 2d XY Model with topological lattice actions, which are invariant against small deformations of the field configuration. These actions constrain the angle between neighbouring spins by an upper bound, or they explicitly suppress vortices (and anti-vortices). Although topological actions do not have a classical limit, they still lead to the universal behaviour of the Berezinskii-Kosterlitz-Thouless (BKT) phase transition — at least up to moderate vortex suppression. In the massive phase, the analytically known Step Scaling Function (SSF) is reproduced in numerical simulations. However, deviations from the expected universal behaviour of the lattice artifacts are observed. In the massless phase, the BKT value of the critical exponent ηc is confirmed. Hence, even though for some topological actions vortices cost zero energy, they still drive the standard BKT transition. In addition we identify a vortex-free transition point, which deviates from the BKT behaviour.

•Jan 1, 2013•6 citations
We numerically investigate the static properties of the two-dimensional (2D) XY-model on the Voronoi–Delaunay lattice, with average connectivity . The critical temperature, magnetization and vortex density are obtained. For instance, in this lattice the critical temperature, above which free vortices take place, reads TVDcr ≈ 1.22 (in units of J, the exchange constant), higher than their counterparts for regular square, TSLcr ≈ 0.79, and triangular lattices TTLcr ≈ 1.156, with constant connectivity given by 4 and 6, respectively. Such results lead us to argue that not only the connectivity number but also how the sites are distributed and linked among themselves is also important for determining these physical quantities.
The critical properties of the spin-1 Blume-Capel model in two dimensions is studied on Voronoi-Delaunay random lattices with quenched connectivity disorder. The system is treated by applying Monte Carlo simulations using the heat-bath update algorithm together with single histograms re-weighting techniques. We calculate the critical temperature as well as the critical exponents as a function of the crystal field $\mathrm{\ensuremath{\Delta}}$. It is found that this disordered system exhibits phase transitions of first- and second-order types that depend on the value of the crystal field. For values of $\mathrm{\ensuremath{\Delta}}\ensuremath{\le}3$, where the nearest-neighbor exchange interaction JJJ has been set to unity, the disordered system presents a second-order phase transition. The results suggest that the corresponding exponent ratio belongs to the same universality class as the regular two-dimensional ferromagnetic model. There exists a tricritical point close to ${\mathrm{\ensuremath{\Delta}}}_{t}=3.05(4)$ with different critical exponents. For ${\mathrm{\ensuremath{\Delta}}}_{t}\ensuremath{\le}\mathrm{\ensuremath{\Delta}}<3.4$ this model undergoes a first-order phase transition. Finally, for $\mathrm{\ensuremath{\Delta}}\ensuremath{\ge}3.4$ the system is always in the paramagnetic phase.
Two-dimensional generalized XY spin model on a triangular lattice is studied by means of Monte-Carlo simulations. The critical temperatures of Berezinskii-Kosterlitz-Thouless (BKT) phase transition are obtained by the method of helicity modulus. It is found that the results are consistent with those obtained by other methods. The vortex density and the vortex-antivortex pair formation energy are also obtained. The result shows that the critical temperature decreases with the increase of the generalization parameter q . While the vortex-antivortex pair formation energy increases with the increase of q when q>1 .
We use the single-cluster Monte Carlo update algorithm to simulate the Ising model on two-dimensional Poissonian random lattices with up to 80 000 sites which are linked together according to the Voronoi-Delaunay prescription. In one set of simulations we use reweighting techniques and finite-size scaling analysis to investigate the critical properties of the model in the very vicinity of the phase transition. In the other set of simulations we study the approach to criticality in the disordered phase, making use of improved estimators for measurements. From both sets of simulations we obtain clear evidence that the critical exponents agree with the exactly known exponents for regular lattices, i.e., that (lattice) universality holds for the two-dimensional Ising model.
We consider the 2d XY Model with topological lattice actions, which are invariant against small deformations of the field configuration. These actions constrain the angle between neighbouring spins by an upper bound, or they explicitly suppress vortices (and anti-vortices). Although topological actions do not have a classical limit, they still lead to the universal behaviour of the Berezinskii-Kosterlitz-Thouless (BKT) phase transition — at least up to moderate vortex suppression. In the massive phase, the analytically known Step Scaling Function (SSF) is reproduced in numerical simulations. However, deviations from the expected universal behaviour of the lattice artifacts are observed. In the massless phase, the BKT value of the critical exponent ηc is confirmed. Hence, even though for some topological actions vortices cost zero energy, they still drive the standard BKT transition. In addition we identify a vortex-free transition point, which deviates from the BKT behaviour.