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).

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.

THE SIMULATION OF THE 2D FERROMAGNETIC BLUME–CAPEL MODEL ON A CELLULAR AUTOMATON

2001 ◽  
Vol 12 (09) ◽  
pp. 1401-1413 ◽  
Author(s):  
B. KUTLU
Keyword(s):  
Critical Temperature ◽  
Cellular Automaton ◽  
Critical Behavior ◽  
Critical Exponents ◽  
Finite Size ◽  
Scaling Theory ◽  
Square Lattice ◽  
Two Dimensional ◽  
Finite Size Scaling ◽  
Creutz Cellular Automaton

The two-dimensional ferromagnetic Blume–Capel model is simulated on a cellular automaton, which based on the Creutz cellular automaton for square lattice. The values of the critical temperature and the static critical exponents are estimated within the framework of the finite-size scaling theory for 0 ≤ D/J ≤ 1.5. The results are compatible with the universal Ising critical behavior.

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.

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