THE RESTRICTED SPIN MODEL

1990 ◽  
Vol 04 (16) ◽  
pp. 1029-1041
Author(s):  
H.A. FARACH ◽  
R.J. CRESWICK ◽  
C.P. POOLE
Keyword(s):  
Monte Carlo ◽  
Critical Temperature ◽  
Heisenberg Model ◽  
Anisotropy Parameter ◽  
Finite Size ◽  
Universality Class ◽  
Spin Model ◽  
Scaling Analysis ◽  
Finite Size Scaling ◽  
Monte Carlo Calculations

We present a novel anisotropic Heisenberg model in which the classical spin is restricted to a region of the unit sphere which depends on the value of the anisotropy parameter Δ. In the limit Δ→1, we recover the Ising model, and in the limit Δ→0, the isotopic Heisenberg model. Monte Carlo calculations are used to compare the critical temperature as a function of the anisotropy parameter for the restricted and unrestricted models, and finite-size scaling analysis leads to the conclusion that for all Δ>0 the model belongs to the Ising universality class. For small A the critical behavior is clearly seen in histograms of the transverse and longitudinal (z) components of the magnetization.

scholarly journals Critical Behaviour of the Ising S=l/2 and S=l Model on (3,4,6,4) and (3,3,3,3,6) Archimedean Lattices

2011 ◽  
Vol 10 (4) ◽  
pp. 912-919 ◽  
Author(s):  
F. W. S. Lima ◽  
J. Mostowicz ◽  
K. Malarz
Keyword(s):  
Monte Carlo ◽  
Critical Temperature ◽  
Monte Carlo Simulations ◽  
Critical Exponents ◽  
Finite Size ◽  
Square Lattice ◽  
Scaling Analysis ◽  
Critical Properties ◽  
Finite Size Scaling ◽  
Effective Dimensionality

AbstractWe investigate the critical properties of the Ising S = 1/2 and S = 1 model on (3,4,6,4) and (34,6) Archimedean lattices. The system is studied through the extensive Monte Carlo simulations. We calculate the critical temperature as well as the critical point exponents γ/ν, β/ν, and ν basing on finite size scaling analysis. The calculated values of the critical temperature for S = 1 are kBTC/J=1.590(3), and kBTC/J=2.100(4) for (3,4,6,4) and (34,6) Archimedean lattices, respectively. The critical exponents β/ν, γ/ν, and 1/ν, for S=1 are β/ν=0.180(20), γ/ν=1.46(8), and 1/ν=0.83(5), for (3,4,6,4) and 0.103(8), 1.44(8), and 0.94(5), for (34,6) Archimedean lattices. Obtained results differ from the Ising S = 1/2 model on (3,4,6,4), (34,6) and square lattice. The evaluated effective dimensionality of the system for S = 1 are Deff=1.82(4), for (3,4,6,4), and Deff = 1.64(5) for (34,6).

scholarly journals Berezinskii-Kosterlitz-Thouless phase transition from lattice sine-Gordon model

2018 ◽  
Vol 175 ◽  
pp. 14003
Author(s):  
Joel Giedt ◽  
James Flamino
Keyword(s):  
Phase Transition ◽  
Monte Carlo ◽  
Critical Temperature ◽  
Finite Size ◽  
Monte Carlo Algorithm ◽  
Finite Size Scaling ◽  
Hybrid Monte Carlo ◽  
Lattice Field ◽  
Autocorrelation Time ◽  
Sine Gordon Model

We obtain nonperturbative results on the sine-Gordon model using the lattice field technique. In particular, we employ the Fourier accelerated hybrid Monte Carlo algorithm for our studies. We find the critical temperature of the theory based autocorrelation time, as well as the finite size scaling of the “thickness” observable used in an earlier lattice study by Hasenbusch et al.

HIGH-PRECISION MONTE CARLO DETERMINATION OF α/ν IN THE 3D CLASSICAL HEISENBERG MODEL

1994 ◽  
Vol 05 (02) ◽  
pp. 267-270
Author(s):  
CHRISTIAN HOLM ◽  
WOLFHARD JANKE
Keyword(s):  
Monte Carlo ◽  
Specific Heat ◽  
Heisenberg Model ◽  
Three Dimensional ◽  
Finite Size ◽  
Topological Defects ◽  
Accurate Estimate ◽  
Scaling Analysis ◽  
Classical Heisenberg Model ◽  
Cluster Monte Carlo

To study the role of topological defects in the three-dimensional classical Heisenberg model we have simulated this model on simple cubic lattices of size up to 803, using the single-cluster Monte Carlo update. Analysing the specific-heat data of these simulations, we obtain a very accurate estimate for the ratio of the specific-heat exponent with the correlation-length exponent, α/ν, from a usual finite-size scaling analysis at the critical coupling Kc. Moreover, by fitting the energy at Kc, we reduce the error estimates by another factor of two, and get a value of α/ν, which is comparable in accuracy to best field theoretic estimates.

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.

scholarly journals CRITICAL BEHAVIOR OF AN EPIDEMIC MODEL OF DRUG RESISTANT DISEASES

2004 ◽  
Vol 15 (09) ◽  
pp. 1279-1290 ◽  
Author(s):  
C. R. DA SILVA ◽  
U. L. FULCO ◽  
M. L. LYRA ◽  
G. M. VISWANATHAN
Keyword(s):  
Critical Behavior ◽  
Finite Size ◽  
Universality Class ◽  
Active Phase ◽  
Propagation Model ◽  
Mutation Rates ◽  
Scaling Analysis ◽  
Directed Percolation ◽  
Drug Resistant ◽  
Finite Size Scaling

In this work, we study the critical behavior of an epidemic propagation model that considers individuals that can develop drug resistance. In our lattice model, each site can be found in one of the four states: empty, healthy, normally infected (not drug resistant) and strain infected (drug resistant) states. The most relevant parameters in our model are related to the mortality, cure and mutation rates. This model presents two distinct stationary active phases: a phase with co-existing normal and drug resistant infected individuals, and an intermediate active phase with only drug resistant individuals. We employed a finite-size scaling analysis to compute the critical points and the critical exponents, β/ν and 1/ν, governing the phase transitions between these active states and the absorbing inactive state. Our results are consistent with the hypothesis that these transitions belong to the directed percolation universality class.

THERMALLY DILUTED ISING SYSTEMS

Fractals ◽  
2003 ◽  
Vol 11 (supp01) ◽  
pp. 53-65
Author(s):  
MANUEL I. MARQUÉS ◽  
JULIO A. GONZALO ◽  
JORGE ÍÑIGUEZ
Keyword(s):  
Critical Temperature ◽  
Ising Model ◽  
Disordered Systems ◽  
Short Range ◽  
Finite Size ◽  
Universality Class ◽  
Finite Size Scaling ◽  
Local Distribution ◽  
Ising Systems ◽  
Theoretical Predictions

In this paper finite size scaling techniques are used to study the universality class of thermally diluted Ising systems, in which the realization of the disposition of magnetic atoms and vacancies is taken from the local distribution of spins in the pure original Ising model at criticality. The critical temperature, the critical exponents and therefore the universality class of these thermally diluted Ising systems depart markedly from the ones of short range correlated disordered systems. This result is in agreement with theoretical predictions previously made by Weinrib and Halperin for systems with long range correlated disorder.

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