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

Physical Review Letters

Potts Model with Long-Range Interactions in One Dimension

E. Bayong, H. T. Diep, Виктор Степанович Доценко

Published Jul 5, 1999• 40 citations
Publisher

Abstract

We study the nature of the phase transition of the $q$-state Potts model with long-range ferromagnetic interactions decaying as $1/{r}^{d+\ensuremath{\sigma}}$, in dimension $d\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}1$, using a histogram Monte Carlo (MC) technique. The model can exhibit a first-order transition or a second-order phase transition with nonstandard critical exponents. The critical value of $q$ above which a first-order transition occurs decreases with decreasing $\ensuremath{\sigma}$, from ${q}_{c}\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}8$ for $\ensuremath{\sigma}\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}1$ to ${q}_{c}\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}2$ for $\ensuremath{\sigma}\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}0.3$. Detailed results for various $\ensuremath{\sigma}$ will be shown and discussed. Mean-field calculation confirms the tendency of our MC results.

DOI
10.1103/physrevlett.83.14

Related papers

Potts model with algebraically decaying interactions in two dimensions

E. Bayong, H. T. Diep

We study the 2d Potts model with long-range interaction algebraically decayed as 1/rd+σ using extensive Monte Carlo simulations to determine the nature of the phase transition with histogram technique. The model is shown to exhibit either a first-order transition or a second-order phase transition with critical exponents depending on σ and q. For q=3 there is a critical value of σ below which a first-order transition occurs. For q⩾5 the transition is of first order for any σ.

Journal of Applied Physics•May 1, 2000•0 citations

First-order phase transition in $1d$ Potts model with long-range interactions

Katarina Uzelac, Zvonko Glumac

The first-order phase transition in the one-dimensional $q$-state Potts model with long-range interactions decaying with distance as $1/r^{1+σ}$ has been studied by Monte Carlo numerical simulations for $0 < σ\le 1$ and integer values of $q > 2$. On the basis of finite-size scaling analysis of interface free energy $ΔF_L$, specific heat and Binder's fourth order cumulant, we obtain the first-order transition which occurs for $σ$ below a threshold value $σ_c(q)$.

arXiv:cond-mat/9807416•Fizika B•Jul 31, 1998•3 citations

Effect of long-range interactions on the critical behavior of the continuous Ising model

E. Bayong, H. T. Diep

Critical behavior of the one- and two-dimensional general continuous Ising models with long-range ferromagnetic interactions decaying as ${1/r}^{d+\ensuremath{\sigma}}$ is studied using a histogram Monte Carlo technique. A continuous Ising model means that a spin can take any value between $\ensuremath{-}1$ and 1. It is found that the system exhibits a second-order phase transition with nonstandard critical exponents which depend on $\ensuremath{\sigma}.$ Results for various values of $\ensuremath{\sigma}$ will be shown and compared to predictions from renormalization-group theory. Though there is an agreement with the overall tendency predicted, there are several fundamental differences. Discussion is given.

Physical review. B, Condensed matter•May 1, 1999•28 citations

Phase transition in a general continuous Ising model with long-range interactions

E. Bayong, H. T. Diep, Trong Tuong Truong

Critical exponents for a one-dimensional general continuous Ising model with long-range ferromagnetic interactions decaying as 1/r1+σ are calculated using a histogram Monte Carlo technique. A continuous Ising model means that a spin can take any value between −1 and 1. The critical point behavior is investigated. It is found that the system exhibits a second-order phase transition with nonstandard critical exponents; the singularities in the specific heat and susceptibility depend on σ. For σ=1, there are extremely weak finite size effects: the first-order and the second-order cumulants of the order parameter yield ν=2.42(1). The susceptibility exponent γ=2.259(9). Results for σ=0.7 will be shown and discussed.

Journal of Applied Physics•Apr 15, 1999•5 citations

Emergent O(n) Symmetry in a Series of 3D Potts Models

Chengxiang Ding, Henk W. J. Blöte, Youjin Deng

We study the q-state Potts model on the simple cubic lattice with ferromagnetic interactions along one lattice direction, and antiferromagnetic interactions along the two other directions. As the temperature T decreases, the system undergoes a second-order phase transition that fits in the universality class of the 3D O(n) model with n=q-1. This conclusion is based on the estimated critical exponents, and histograms of the order parameter. At even smaller T we find, for q=4 and 5, a first-order transition to a phase with a different type of long-range order. This long-range order dissolves at T=0, and the system effectively reduces to a disordered two-dimensional Potts antiferromagnet. These results are obtained by means of Monte Carlo simulations and finite-size scaling.

•Aug 19, 2015•0 citations

Reexamination of the long-range Potts model: A multicanonical approach

Sylvain Reynal, H. T. Diep

We investigate the critical behavior of the one-dimensional q-state Potts model with long-range (LR) interactions 1/r(d+sigma), using a multicanonical algorithm. The recursion scheme initially proposed by Berg is improved so as to make it suitable for a large class of LR models with unequally spaced energy levels. The choice of an efficient predictor and a reliable convergence criterion is discussed. We obtain transition temperatures in the first-order regime which are in far better agreement with mean-field predictions than in previous Monte Carlo studies. By relying on the location of spinodal points and resorting to scaling arguments, we determine the threshold value sigma(c)(q) separating the first- and second-order regimes to two-digit precision within the range 3< or =q < or =9. We offer convincing numerical evidence supporting sigma(c)(q)<1.0 for all q, by virtue of an unusual finite-size effect, namely, finite-size scaling predicts a continuous transition in the thermodynamic limit, despite the first-order nature of the transition at finite size. A qualitative account in terms of correlation lengths is provided. Finally, we find the crossover between the LR and short-range regimes to occur inside a narrow window 1.0<sigma<1.2, thus lending strong support to Sak's scenario.

arXiv:cond-mat/0306493•Physical Review E•Feb 24, 2004•15 citations
We study the nature of the phase transition of the qqq-state Potts model with long-range ferromagnetic interactions decaying as 1/rd+\ensuremathσ1/{r}^{d+\ensuremath{\sigma}}1/rd+\ensuremathσ, in dimension d=1d\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}1d=1, using a histogram Monte Carlo (MC) technique. The model can exhibit a first-order transition or a second-order phase transition with nonstandard critical exponents. The critical value of qqq above which a first-order transition occurs decreases with decreasing \ensuremathσ\ensuremath{\sigma}\ensuremathσ, from qc=8{q}_{c}\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}8qc​=8 for \ensuremathσ=1\ensuremath{\sigma}\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}1\ensuremathσ=1 to qc=2{q}_{c}\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}2qc​=2 for \ensuremathσ=0.3\ensuremath{\sigma}\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}0.3\ensuremathσ=0.3. Detailed results for various \ensuremathσ\ensuremath{\sigma}\ensuremathσ will be shown and discussed. Mean-field calculation confirms the tendency of our MC results.
First-order phase transition in 1d1d1d Potts model with long-range interactions
The first-order phase transition in the one-dimensional qqq-state Potts model with long-range interactions decaying with distance as 1/r1+σ1/r^{1+σ}1/r1+σ has been studied by Monte Carlo numerical simulations for 0<σ≤10 < σ\le 10<σ≤1 and integer values of q>2q > 2q>2. On the basis of finite-size scaling analysis of interface free energy ΔFLΔF_LΔFL​, specific heat and Binder's fourth order cumulant, we obtain the first-order transition which occurs for σσσ below a threshold value σc(q)σ_c(q)σc​(q).
Critical behavior of the one- and two-dimensional general continuous Ising models with long-range ferromagnetic interactions decaying as ${1/r}^{d+\ensuremath{\sigma}}$ is studied using a histogram Monte Carlo technique. A continuous Ising model means that a spin can take any value between $\ensuremath{-}1$ and 1. It is found that the system exhibits a second-order phase transition with nonstandard critical exponents which depend on $\ensuremath{\sigma}.$ Results for various values of $\ensuremath{\sigma}$ will be shown and compared to predictions from renormalization-group theory. Though there is an agreement with the overall tendency predicted, there are several fundamental differences. Discussion is given.
Critical exponents for a one-dimensional general continuous Ising model with long-range ferromagnetic interactions decaying as 1/r1+σ are calculated using a histogram Monte Carlo technique. A continuous Ising model means that a spin can take any value between −1 and 1. The critical point behavior is investigated. It is found that the system exhibits a second-order phase transition with nonstandard critical exponents; the singularities in the specific heat and susceptibility depend on σ. For σ=1, there are extremely weak finite size effects: the first-order and the second-order cumulants of the order parameter yield ν=2.42(1). The susceptibility exponent γ=2.259(9). Results for σ=0.7 will be shown and discussed.
We study the q-state Potts model on the simple cubic lattice with ferromagnetic interactions along one lattice direction, and antiferromagnetic interactions along the two other directions. As the temperature T decreases, the system undergoes a second-order phase transition that fits in the universality class of the 3D O(n) model with n=q-1. This conclusion is based on the estimated critical exponents, and histograms of the order parameter. At even smaller T we find, for q=4 and 5, a first-order transition to a phase with a different type of long-range order. This long-range order dissolves at T=0, and the system effectively reduces to a disordered two-dimensional Potts antiferromagnet. These results are obtained by means of Monte Carlo simulations and finite-size scaling.
We investigate the critical behavior of the one-dimensional q-state Potts model with long-range (LR) interactions 1/r(d+sigma), using a multicanonical algorithm. The recursion scheme initially proposed by Berg is improved so as to make it suitable for a large class of LR models with unequally spaced energy levels. The choice of an efficient predictor and a reliable convergence criterion is discussed. We obtain transition temperatures in the first-order regime which are in far better agreement with mean-field predictions than in previous Monte Carlo studies. By relying on the location of spinodal points and resorting to scaling arguments, we determine the threshold value sigma(c)(q) separating the first- and second-order regimes to two-digit precision within the range 3< or =q < or =9. We offer convincing numerical evidence supporting sigma(c)(q)<1.0 for all q, by virtue of an unusual finite-size effect, namely, finite-size scaling predicts a continuous transition in the thermodynamic limit, despite the first-order nature of the transition at finite size. A qualitative account in terms of correlation lengths is provided. Finally, we find the crossover between the LR and short-range regimes to occur inside a narrow window 1.0<sigma<1.2, thus lending strong support to Sak's scenario.