Nonequilibrium model on Archimedean lattices

Open Physics ◽  
2014 ◽  
Vol 12 (3) ◽  
Author(s):  
F. Lima
Keyword(s):  
Majority Vote ◽  
Finite Size ◽  
Stat Phys ◽  
Critical Properties ◽  
Finite Size Scaling ◽  
Critical Temperatures ◽  
Vote Model ◽  
Monte Carlo Studies ◽  
Regular Lattices ◽  
Binder Cumulant

AbstractOn (4, 6, 12) and (4, 82) Archimedean lattices, the critical properties of the majority-vote model are considered and studied using the Glauber transition rate proposed by Kwak et al. [Kwak et al., Phys. Rev. E, 75, 061110 (2007)] rather than the traditional majority-vote with noise [Oliveira, J. Stat. Phys. 66, 273 (1992)]. We obtain T c and the critical exponents for this Glauber rate from extensive Monte Carlo studies and finite size scaling. The calculated values of the critical temperatures and Binder cumulant are T c = 0.651(3) and U 4* = 0.612(5), and T c = 0.667(2) and U 4* = 0.613(5), for (4, 6, 12) and (4, 82) lattices respectively, while the exponent (ratios) β/ν, γ/ν and 1/ν are respectively: 0.105(8), 1.48(11) and 1.16(5) for (4, 6, 12); and 0.113(2), 1.60(4) and 0.84(6) for (4, 82) lattices. The usual Ising model and the majority-vote model on previously studied regular lattices or complex networks differ from our new results.

scholarly journals MAJORITY-VOTE MODEL WITH HETEROGENEOUS AGENTS ON SQUARE LATTICE

2013 ◽  
Vol 24 (11) ◽  
pp. 1350083 ◽  
Author(s):  
F. W. S. LIMA
Keyword(s):  
Heterogeneous Agents ◽  
Majority Vote ◽  
Finite Size ◽  
Universality Class ◽  
Square Lattice ◽  
Stat Phys ◽  
Finite Size Scaling ◽  
Vote Model ◽  
Noise Parameter ◽  
Binder Cumulant

We study a nonequilibrium model with up-down symmetry and a noise parameter q known as majority-vote model (MVM) of [M. J. Oliveira, J. Stat. Phys.66, 273 (1992)] with heterogeneous agents on square lattice (SL). By Monte Carlo (MC) simulations and finite-size scaling relations, the critical exponents β∕ν, γ∕ν and 1∕ν and points qc and U* are obtained. After extensive simulations, we obtain β∕ν = 0.35(1), γ∕ν = 1.23(8) and 1∕ν = 1.05(5). The calculated values of the critical noise parameter and Binder cumulant are qc = 0.1589(4) and U* = 0.604(7). Within the error bars, the exponents obey the relation 2β∕ν + γ∕ν = 2 and the results presented here demonstrate that the MVM heterogeneous agents belongs to a different universality class than the nonequilibrium MVM with homogeneous agents on SL.

scholarly journals MAJORITY-VOTE MODEL ON OPINION-DEPENDENT NETWORK

2013 ◽  
Vol 24 (09) ◽  
pp. 1350066 ◽  
Author(s):  
F. W. S. LIMA
Keyword(s):  
Monte Carlo ◽  
Majority Vote ◽  
Finite Size ◽  
Universality Class ◽  
Scaling Relations ◽  
Finite Size Scaling ◽  
Vote Model ◽  
Noise Parameter ◽  
Error Bars ◽  
Binder Cumulant

We study a nonequilibrium model with up–down symmetry and a noise parameter q known as majority-vote model (MVM) of Oliveira 1992 on opinion-dependent network or Stauffer–Hohnisch–Pittnauer (SHP) networks. By Monte Carlo (MC) simulations and finite-size scaling relations the critical exponents β∕ν, γ∕ν and 1∕ν and points qc and U* are obtained. After extensive simulations, we obtain β∕ν = 0.230(3), γ∕ν = 0.535(2) and 1∕ν = 0.475(8). The calculated values of the critical noise parameter and Binder cumulant are qc = 0.166(3) and U* = 0.288(3). Within the error bars, the exponents obey the relation 2β∕ν + γ∕ν = 1 and the results presented here demonstrate that the MVM belongs to a different universality class than the equilibrium Ising model on SHP networks, but to the same class as majority-vote models on some other networks.

BERRY PHASE AND CRITICAL BEHAVIOR OF THE XY SPIN CHAIN WITH THREE-SITE INTERACTION

2012 ◽  
Vol 26 (22) ◽  
pp. 1250141 ◽  
Author(s):  
HANLI LIAN
Keyword(s):  
Spin Chain ◽  
Berry Phase ◽  
Finite Size ◽  
Transverse Magnetic ◽  
Anomalous Behavior ◽  
Quantum Criticality ◽  
Critical Properties ◽  
Finite Size Scaling ◽  
Surrounding Environment ◽  
Xy Spin Chain

By calculating the Berry Phase (BP) of a central spin, the quantum criticality of the surrounding environment described by an XY spin chain with the three-site interaction in a transverse magnetic field is explored. The BP presents anomalous behavior along the critical region. The finite-size scaling behaviors suggest that the BP of the central spin can well capture the critical properties of the XY spin chain with the three-site interaction.

Equilibrium and nonequilibrium models on solomon networks with two square lattices

2017 ◽  
Vol 28 (08) ◽  
pp. 1750099
Author(s):  
F. W. S. Lima
Keyword(s):  
Monte Carlo ◽  
Monte Carlo Simulations ◽  
Critical Exponent ◽  
Critical Points ◽  
Majority Vote ◽  
Universality Class ◽  
2D Systems ◽  
Two Dimensional ◽  
Critical Properties ◽  
Regular Lattices

We investigate the critical properties of the equilibrium and nonequilibrium two-dimensional (2D) systems on Solomon networks with both nearest and random neighbors. The equilibrium and nonequilibrium 2D systems studied here by Monte Carlo simulations are the Ising and Majority-vote 2D models, respectively. We calculate the critical points as well as the critical exponent ratios [Formula: see text], [Formula: see text], and [Formula: see text]. We find that numerically both systems present the same exponents on Solomon networks (2D) and are of different universality class than the regular 2D ferromagnetic model. Our results are in agreement with the Grinstein criterion for models with up and down symmetry on regular lattices.

A FINITE-SIZE SCALING STUDY OF THE FOUR-DIMENSIONAL ISING MODEL ON THE CREUTZ CELLULAR AUTOMATON

1999 ◽  
Vol 10 (05) ◽  
pp. 875-881 ◽  
Author(s):  
N. AKTEKIN ◽  
A. GÜNEN ◽  
Z. SAĞLAM
Keyword(s):  
Magnetic Susceptibility ◽  
Ising Model ◽  
Cellular Automaton ◽  
Specific Heat ◽  
Finite Size ◽  
Scaling Relations ◽  
Finite Size Scaling ◽  
Critical Temperatures ◽  
Size Scaling ◽  
Creutz Cellular Automaton

The four-dimensional Ising model is simulated on the Creutz cellular automaton with increased precision. The data are analyzed according to the finite-size scaling relations available. The precision of the critical values related to magnetic susceptibility is improved by one digit, but in order to reach to the same precision for those related to the specific heat more simulation runs at the critical temperatures of the finite-size lattices are required.

Majority-vote model on directed Small-World-Voronoi–Delaunay random lattices

2018 ◽  
Vol 29 (07) ◽  
pp. 1850061
Author(s):  
R. S. C. Brenda ◽  
F. W. S. Lima
Keyword(s):  
Critical Exponents ◽  
Majority Vote ◽  
Small World ◽  
Universality Class ◽  
Two Dimensions ◽  
Critical Properties ◽  
Disordered System ◽  
Vote Model ◽  
Random Lattices ◽  
Second Order Phase Transition

We investigate the critical properties of the nonequilibrium majority-vote model in two-dimensions on directed small-world lattice with quenched connectivity disorder. The disordered system is studied through Monte Carlo simulations: the critical noise ([Formula: see text]), as well as the critical exponents [Formula: see text], [Formula: see text], and [Formula: see text] for several values of the rewiring probability [Formula: see text]. We find that this disordered system does not belong to the same universality class as the regular two-dimensional ferromagnetic model. The majority-vote model on directed small-world lattices presents in fact a second-order phase transition with new critical exponents which do not depend on [Formula: see text] ([Formula: see text]), but agree with the exponents of the equilibrium Ising model on directed small-world Voronoi–Delaunay random lattices.

Finite-size scaling in ferromagnetic spin systems on the pyrochlore lattice

2020 ◽  
pp. 255-266
Author(s):  
K.S. Soldatov ◽  
◽  
M.A. Padalko ◽  
V.S. Strongin ◽  
D.Yu. Kapitan ◽  
...  
Keyword(s):  
Heisenberg Model ◽  
High Performance ◽  
Finite Size ◽  
Spin Systems ◽  
Xy Model ◽  
Finite Size Scaling ◽  
Critical Temperatures ◽  
Cluster Algorithms ◽  
Size Scaling ◽  
Classical Heisenberg Model

In this paper we present the results of the high-performance computations for the Ising model, the XY-model and the classical Heisenberg model for the pyrochlore lattice. We used Wolff and Swendsen-Wang cluster algorithms with GPU parallelization for the calculations. We obtained critical exponents and critical temperatures using finite-size scaling approach.

Sign in / Sign up

Export Citation Format

Share Document