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:0806.2432 · Physical Review B

Tricritical transition in the classical XY model on the kagome lattice under local anisotropy

Farhad Shahbazi, Saba Mortezapour

Published Jun 13, 2008• 3 citations
arXivHTMLPDF

Abstract

Using mean-field theory and high-resolution Monte Carlo simulation technique based on multihistogram method, we have investigated the critical properties of an antiferromagnetic $XY$ model on the two-dimensional (2D) kagome lattice, with single-ion easy-axes anisotropy. The mean-field theory predicts second-order phase transition from disordered to all-in all-out state for any value of anisotropy for this model. However, Monte Carlo simulations result in first-order transition for small values of anisotropy, which turns to second order with increasing strength of anisotropy, indicating the existence of a tricritical point for this model. The critical exponents, obtained by finite-size scaling methods, show that the transition is in Ising universality class for large values of anisotropy, while the critical behavior of the system deviates from 2D ${\ensuremath{\phi}}^{6}$ model near the tricritical point. This suggests the possibility for existence of another tricritical universality in two dimensions.

DOI
10.1103/physrevb.77.214420

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

Dynamic phase transitions on the kagome Ising ferromagnet

Zeynep Demir Vatansever

We perform extensive Monte Carlo simulations to investigate the dynamic phase transition properties of the two-dimensional kinetic Ising model on the kagome lattice in the presence of square-wave oscillating magnetic field. Through detailed finite-size scaling analysis, we study universality aspects of the nonequilibrium phase transition. Obtained critical exponents indicate that the two-dimensional kagome-lattice kinetic Ising model belongs to the same universality class with the corresponding Ising model in equilibrium. Moreover, dynamic critical exponent of the local moves used in simulations is determined with high precision. Our numerical results are compatible with the previous ones on kinetic Ising models.

arXiv:2211.01709•Physical review. E•Nov 18, 2022•12 citations

Finite Size Scaling of the 2D Six-Clock model

M. Itakura, Trieste (Italy) International School for Advanced Studies

We investigate the isotropic-anisotropic phase transition of the twodimensional XY model with six-fold anisotropy, using Monte Carlo renormalization group method. The result indicates difficulty of observing asymptotic critical behavior in Monte Carlo simulations, owing to the marginal flow at the fixed point. PACS numbers: 02.70.Lq, 75.10.Hk Typeset using REVTEX 1 The XY model with Z6 symmetry breaking field represents not only planar spin magnets with Z6 symmetric crystal field [1], but also models with Z2 × Z3 symmetry (which is isomorphic to Z6) such as three-state antiferromagnetic Potts model on the square and the cubic lattice [2] and Ising antiferromagnet on the triangular and the stacked-triangular lattice [3–8]. The critical behavior of the model in two dimension is well understood by scaling argument [1]: The model undergoes two distinct phase transitions, both of which being

•Jan 1, 2001•2 citations

Universality and tricritical behavior of three-dimensional Ising models with two- and four-spin interactions

Ole G. Mouritsen, Svend J. Knak Jensen, B. Frank

The Monte Carlo technique is applied to a study of the phase transitions and the critical behavior of the spin-\textonehalf{} Ising model on an fcc lattice with mixtures of two- (${J}_{2}$) and four - (${J}_{4}$) spin interactions. In the limit ${J}_{2}=0$ the model exhibits a first-order transition. The transition remains of first order for $\frac{{J}_{4}}{{J}_{2}}\ensuremath{\gtrsim}\frac{1}{2}$, but a crossover to continuous transitions is found around $\frac{{J}_{4}}{{J}_{2}}\ensuremath{\approx}\frac{1}{4}\ensuremath{-}\frac{1}{2}$ indicating that the model exhibits tricritical behavior. A modified mean-field theory is presented leading to an approximate description of the tricritical behavior in agreement with the Monte Carlo calculations. In the region of continuous transitions. $0<~\frac{{J}_{4}}{{J}_{2}}\ensuremath{\lesssim}\frac{1}{4}$, the critical exponent $\ensuremath{\beta}$ pertaining to the order parameter derived from the Monte Carlo data retains the Ising value, in accordance with the universality hypothesis. Our findings show that the four-spin interactions do not lead to nonuniversal critical behavior, contrary to the conclusions made by Griffiths and Wood from a series analysis.

Physical review. B, Condensed matter•Jul 1, 1981•27 citations

Histogram Monte Carlo study of the next-nearest-neighbor Ising antiferromagnet on a stacked triangular lattice

M. L. Plumer, Alain Mailhot, R. Ducharme +2 more

Critical properties of the Ising model on a stacked triangular lattice, with antiferromagnetic first- and second-neighbor in-plane interactions, are studied by extensive histogram Monte Carlo simulations. The results, in conjunction with the recently determined phase diagram, strongly suggest that the transition from the period-3 ordered state to the paramagnetic phase remains in the XY universality class. This conclusion is in contrast with a previous suggestion of mean-field tricritical behavior.

arXiv:cond-mat/9301028•Physical review. B, Condensed matter•Jun 1, 1993•33 citations

Metropolis Monte Carlo and Wang-Landau Simulations of Tricriticality in Crossed Ising Chains

Tyler Cary, Rajiv R. P. Singh, Richard Scalettar

We explore the phase diagram of Ising spins on one-dimensional chains which criss-cross in two perpendicular directions and are connected by interchain couplings. This system is of interest as a simpler, classical analog of a quantum Hamiltonian which has been proposed as a model of magnetic behavior in Nb$_{12}$O$_{29}$ and also, conceptually, as a geometry which is intermediate between one and two dimensions. Using mean field theory as well as Metropolis Monte Carlo and Wang-Landau simulations, we locate quantitatively the boundaries of four ordered phases. Each becomes an effective Ising model with unique effective couplings at large interchain coupling. Away from this limit we demonstrate non-trivial critical behavior, including tricritical points which separate first and second order phase transitions. Finally, we find that the crossover of the magnetization critical exponent from the Ising to tricritical Ising value shows an unusual non-monotonic behavior.

Bulletin of the American Physical Society•Aug 9, 2016•0 citations
Using mean-field theory and high-resolution Monte Carlo simulation technique based on multihistogram method, we have investigated the critical properties of an antiferromagnetic XYXYXY model on the two-dimensional (2D) kagome lattice, with single-ion easy-axes anisotropy. The mean-field theory predicts second-order phase transition from disordered to all-in all-out state for any value of anisotropy for this model. However, Monte Carlo simulations result in first-order transition for small values of anisotropy, which turns to second order with increasing strength of anisotropy, indicating the existence of a tricritical point for this model. The critical exponents, obtained by finite-size scaling methods, show that the transition is in Ising universality class for large values of anisotropy, while the critical behavior of the system deviates from 2D \ensuremathϕ6{\ensuremath{\phi}}^{6}\ensuremathϕ6 model near the tricritical point. This suggests the possibility for existence of another tricritical universality in two dimensions.
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.
We perform extensive Monte Carlo simulations to investigate the dynamic phase transition properties of the two-dimensional kinetic Ising model on the kagome lattice in the presence of square-wave oscillating magnetic field. Through detailed finite-size scaling analysis, we study universality aspects of the nonequilibrium phase transition. Obtained critical exponents indicate that the two-dimensional kagome-lattice kinetic Ising model belongs to the same universality class with the corresponding Ising model in equilibrium. Moreover, dynamic critical exponent of the local moves used in simulations is determined with high precision. Our numerical results are compatible with the previous ones on kinetic Ising models.
We investigate the isotropic-anisotropic phase transition of the twodimensional XY model with six-fold anisotropy, using Monte Carlo renormalization group method. The result indicates difficulty of observing asymptotic critical behavior in Monte Carlo simulations, owing to the marginal flow at the fixed point. PACS numbers: 02.70.Lq, 75.10.Hk Typeset using REVTEX 1 The XY model with Z6 symmetry breaking field represents not only planar spin magnets with Z6 symmetric crystal field [1], but also models with Z2 × Z3 symmetry (which is isomorphic to Z6) such as three-state antiferromagnetic Potts model on the square and the cubic lattice [2] and Ising antiferromagnet on the triangular and the stacked-triangular lattice [3–8]. The critical behavior of the model in two dimension is well understood by scaling argument [1]: The model undergoes two distinct phase transitions, both of which being
The Monte Carlo technique is applied to a study of the phase transitions and the critical behavior of the spin-\textonehalf{} Ising model on an fcc lattice with mixtures of two- (J2{J}_{2}J2​) and four - (J4{J}_{4}J4​) spin interactions. In the limit J2=0{J}_{2}=0J2​=0 the model exhibits a first-order transition. The transition remains of first order for $\frac{{J}_{4}}{{J}_{2}}\ensuremath{\gtrsim}\frac{1}{2}$, but a crossover to continuous transitions is found around $\frac{{J}_{4}}{{J}_{2}}\ensuremath{\approx}\frac{1}{4}\ensuremath{-}\frac{1}{2}$ indicating that the model exhibits tricritical behavior. A modified mean-field theory is presented leading to an approximate description of the tricritical behavior in agreement with the Monte Carlo calculations. In the region of continuous transitions. $0<~\frac{{J}_{4}}{{J}_{2}}\ensuremath{\lesssim}\frac{1}{4}$, the critical exponent $\ensuremath{\beta}$ pertaining to the order parameter derived from the Monte Carlo data retains the Ising value, in accordance with the universality hypothesis. Our findings show that the four-spin interactions do not lead to nonuniversal critical behavior, contrary to the conclusions made by Griffiths and Wood from a series analysis.
Critical properties of the Ising model on a stacked triangular lattice, with antiferromagnetic first- and second-neighbor in-plane interactions, are studied by extensive histogram Monte Carlo simulations. The results, in conjunction with the recently determined phase diagram, strongly suggest that the transition from the period-3 ordered state to the paramagnetic phase remains in the XY universality class. This conclusion is in contrast with a previous suggestion of mean-field tricritical behavior.
We explore the phase diagram of Ising spins on one-dimensional chains which criss-cross in two perpendicular directions and are connected by interchain couplings. This system is of interest as a simpler, classical analog of a quantum Hamiltonian which has been proposed as a model of magnetic behavior in Nb12_{12}12​O29_{29}29​ and also, conceptually, as a geometry which is intermediate between one and two dimensions. Using mean field theory as well as Metropolis Monte Carlo and Wang-Landau simulations, we locate quantitatively the boundaries of four ordered phases. Each becomes an effective Ising model with unique effective couplings at large interchain coupling. Away from this limit we demonstrate non-trivial critical behavior, including tricritical points which separate first and second order phase transitions. Finally, we find that the crossover of the magnetization critical exponent from the Ising to tricritical Ising value shows an unusual non-monotonic behavior.