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/0309001

Short-range type critical behavior in spite of long-range interactions: the phase transition of a Coulomb system on a lattice

Arnulf Möbius, U. Roessler

Published Aug 29, 2003• 1 citation
arXivHTMLPDF

Abstract

One- to three-dimensional hypercubic lattices half-filled with localized particles interacting via the long-range Coulomb potential are investigated numerically. The temperature dependences of specific heat, mean staggered occupation, and of a generalized susceptibility indicate order-disorder phase transitions in two- and three-dimensional systems. The critical properties, clarified by finite-size scaling analysis, are consistent with those of the Ising model with short-range interaction.

DOI
10.48550/arxiv.cond-mat/0309001

Related papers

Critical behavior of the Coulomb-glass model in the zero-disorder limit: Ising universality in a system with long-range interactions

Arnulf Möbius, U. Rößler

The ordering of charges on half-filled hypercubic lattices is investigated numerically, where electroneutrality is ensured by background charges. This system is equivalent to the $s=1/2$ Ising lattice model with antiferromagnetic $1/r$ interaction. The temperature dependences of specific heat, mean staggered occupation, and of a generalized susceptibility indicate continuous order-disorder phase transitions at finite temperatures in two- and three-dimensional systems. In contrast, the susceptibility of the one-dimensional system exhibits singular behavior at vanishing temperature. For the two- and three-dimensional cases, the critical exponents are obtained by means of a finite-size scaling analysis. Their values are consistent with those of the Ising model with short-range interaction, and they imply that the studied model cannot belong to any other known universality class. Samples of up to 1400, ${112}^{2}$, and ${22}^{3}$ sites are considered for dimensions 1 to 3, respectively.

arXiv:0904.3723•Physical Review B•May 21, 2009•20 citations

Critical behavior of the random-field Ising model at and beyond the upper critical dimension

Björn Ahrens, Alexander K. Hartmann

The disorder-driven phase transition of the random-field Ising model is observed using exact ground-state computer simulations for hypercubic lattices in $d=5,6,7$ dimensions. Finite-size scaling analyses are used to calculate the critical point and the critical exponents of the specific heat, magnetization, susceptibility, and of the correlation length. For dimensions $d=6,7$ which are larger or equal to the assumed upper critical dimension, ${d}_{u}=6$, mean-field behavior is found, i.e., $\ensuremath{\alpha}=0, \ensuremath{\beta}=1/2, \ensuremath{\gamma}=1, \ensuremath{\nu}=1/2$. For the analysis of the numerical data, it appears to be necessary to include recently proposed corrections to scaling at and beyond the upper critical dimension.

arXiv:1010.2911•Physical Review B•Jan 31, 2011•32 citations

Phase transition of a one-dimensional Ising model with distance-dependent connections

Yunfeng Chang, Liang Sun, Xu Cai

The critical behavior of the Ising model on a one-dimensional network, which has long-range connections at distances l>1 with the probability theta(l) approximately l(-m), is studied by using Monte Carlo simulations. Through analyzing the Ising model on networks with different m values, this paper discusses the impact of the global correlation, which decays with the increase of m, on the phase transition of the Ising model. Adding the analysis of the finite-size scaling of the order parameter [M], it is observed that in the whole range of 0<m<2, a finite-temperature transition exists, and the critical exponents show consistence with mean-field values, which indicates a mean-field nature of the phase transition.

arXiv:nlin/0703040•Physical Review E•Aug 1, 2007•7 citations

Mutual exclusion statistics and the infinite-range Hubbard model: critical behavior in the quantum regime

Gabriel F. O. Ramos, Weverton Lucas da Silva Rosendo, Ernesto P. Raposo +1 more

Abstract We investigate the critical behavior in the quantum regime of the Hubbard model in d-dimensional hypercubic lattices with infinite-range Coulomb interaction. The Haldane–Wu mutual exclusion statistics approach, which comprises three species of exclusions, allows us to derive the singular part of the free energy, entropy, and specific heat in the quantum regime g > T, where g is the scaling interaction parameter and T is the temperature. We present results from the analytic series expansions of observables near the quantum critical point: T = g = μ = 0 , where µ is the chemical potential. The signature of the mutual exclusion statistics manifests through the appearance of polylogarithms related to Lerch functions in the coefficients of the free energy series in powers of T / g . The calculated critical exponents from the analytic series are consistent with our scaling analysis in the quantum regime. In particular, the specific heat is shown to display a variety of critical behaviors, C / T ∼ g − α g , g → 0 + , depending on the lattice dimension: from a singular behavior in d = 1 ( α g = 1 / 2 ) to a constant value in d = 2 ( α g = 0 ), and regular behavior for d > 2 ( α g = 1 − d / 2 < 0 ).

Journal of Physics A Mathematical and Theoretical•Jan 10, 2025•0 citations

Critical behavior of a cubic-lattice 3D Ising model for systems with quenched disorder

Akai Kurbanovich Murtazaev, Ibragimkhan K. Kamilov, Albert Babaevich Babaev

A Monte Carlo method is applied to simulate the static critical behavior of a cubic-lattice 3D Ising model for systems with quenched disorder. Numerical results are presented for the spin concentrations of p = 1.0, 0.95, 0.9, 0.8, 0.6 on L × L × L lattices with L = 20–60 under periodic boundary conditions. The critical temperature is determined by the Binder cumulant method. A finite-size scaling technique is used to calculate the static critical exponents α, β, γ, and ν (for specific heat, susceptibility, magnetization, and correlation length, respectively) in the range of p under study. Universality classes of critical behavior are discussed for three-dimensional diluted systems.

Journal of Experimental and Theoretical Physics•Dec 1, 2004•35 citations

Second-Order Phase Transition in the Two-Dimensional Classical Lattice Coulomb Gas of Half-Integer Charges

Meng‐Bo Luo, Qing‐Hu Chen, XU ZHU-AN +1 more

The second-order phase transition in the two-dimensional (2D) classical Coulomb gas of half-integer charges on a square lattice is investigated by using Monte Carlo simulations. Based on the finite-size scaling analysis, we estimate the second-order phase transition temperature Tc and the static critical exponents β and ν with a new numerical analysis method. More precise critical temperature Tc = 0.1311(2) and critical exponents β/ν = 0.1152(12) and ν = 0.857(15) are obtained. The estimated value of ν indicates that the charge lattice melting transition is different from the pure 2D Ising transition.

Chinese Physics Letters•Jul 1, 2001•6 citations
One- to three-dimensional hypercubic lattices half-filled with localized particles interacting via the long-range Coulomb potential are investigated numerically. The temperature dependences of specific heat, mean staggered occupation, and of a generalized susceptibility indicate order-disorder phase transitions in two- and three-dimensional systems. The critical properties, clarified by finite-size scaling analysis, are consistent with those of the Ising model with short-range interaction.
The ordering of charges on half-filled hypercubic lattices is investigated numerically, where electroneutrality is ensured by background charges. This system is equivalent to the s=1/2s=1/2s=1/2 Ising lattice model with antiferromagnetic 1/r1/r1/r interaction. The temperature dependences of specific heat, mean staggered occupation, and of a generalized susceptibility indicate continuous order-disorder phase transitions at finite temperatures in two- and three-dimensional systems. In contrast, the susceptibility of the one-dimensional system exhibits singular behavior at vanishing temperature. For the two- and three-dimensional cases, the critical exponents are obtained by means of a finite-size scaling analysis. Their values are consistent with those of the Ising model with short-range interaction, and they imply that the studied model cannot belong to any other known universality class. Samples of up to 1400, 1122{112}^{2}1122, and 223{22}^{3}223 sites are considered for dimensions 1 to 3, respectively.
The disorder-driven phase transition of the random-field Ising model is observed using exact ground-state computer simulations for hypercubic lattices in d=5,6,7d=5,6,7d=5,6,7 dimensions. Finite-size scaling analyses are used to calculate the critical point and the critical exponents of the specific heat, magnetization, susceptibility, and of the correlation length. For dimensions d=6,7d=6,7d=6,7 which are larger or equal to the assumed upper critical dimension, du=6{d}_{u}=6du​=6, mean-field behavior is found, i.e., $\ensuremath{\alpha}=0, \ensuremath{\beta}=1/2, \ensuremath{\gamma}=1, \ensuremath{\nu}=1/2$. For the analysis of the numerical data, it appears to be necessary to include recently proposed corrections to scaling at and beyond the upper critical dimension.
The critical behavior of the Ising model on a one-dimensional network, which has long-range connections at distances l>1 with the probability theta(l) approximately l(-m), is studied by using Monte Carlo simulations. Through analyzing the Ising model on networks with different m values, this paper discusses the impact of the global correlation, which decays with the increase of m, on the phase transition of the Ising model. Adding the analysis of the finite-size scaling of the order parameter [M], it is observed that in the whole range of 0<m<2, a finite-temperature transition exists, and the critical exponents show consistence with mean-field values, which indicates a mean-field nature of the phase transition.
Abstract We investigate the critical behavior in the quantum regime of the Hubbard model in d-dimensional hypercubic lattices with infinite-range Coulomb interaction. The Haldane–Wu mutual exclusion statistics approach, which comprises three species of exclusions, allows us to derive the singular part of the free energy, entropy, and specific heat in the quantum regime g > T, where g is the scaling interaction parameter and T is the temperature. We present results from the analytic series expansions of observables near the quantum critical point: T = g = μ = 0 , where µ is the chemical potential. The signature of the mutual exclusion statistics manifests through the appearance of polylogarithms related to Lerch functions in the coefficients of the free energy series in powers of T / g . The calculated critical exponents from the analytic series are consistent with our scaling analysis in the quantum regime. In particular, the specific heat is shown to display a variety of critical behaviors, C / T ∼ g − α g , g → 0 + , depending on the lattice dimension: from a singular behavior in d = 1 ( α g = 1 / 2 ) to a constant value in d = 2 ( α g = 0 ), and regular behavior for d > 2 ( α g = 1 − d / 2 < 0 ).
A Monte Carlo method is applied to simulate the static critical behavior of a cubic-lattice 3D Ising model for systems with quenched disorder. Numerical results are presented for the spin concentrations of p = 1.0, 0.95, 0.9, 0.8, 0.6 on L × L × L lattices with L = 20–60 under periodic boundary conditions. The critical temperature is determined by the Binder cumulant method. A finite-size scaling technique is used to calculate the static critical exponents α, β, γ, and ν (for specific heat, susceptibility, magnetization, and correlation length, respectively) in the range of p under study. Universality classes of critical behavior are discussed for three-dimensional diluted systems.
The second-order phase transition in the two-dimensional (2D) classical Coulomb gas of half-integer charges on a square lattice is investigated by using Monte Carlo simulations. Based on the finite-size scaling analysis, we estimate the second-order phase transition temperature Tc and the static critical exponents β and ν with a new numerical analysis method. More precise critical temperature Tc = 0.1311(2) and critical exponents β/ν = 0.1152(12) and ν = 0.857(15) are obtained. The estimated value of ν indicates that the charge lattice melting transition is different from the pure 2D Ising transition.