Berezinskii-Kosterlitz-Thouless phase transition from lattice 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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THE RESTRICTED SPIN MODEL

Modern Physics Letters B ◽

10.1142/s0217984990001306 ◽

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.

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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

Communications in Computational Physics ◽

10.4208/cicp.090910.021210a ◽

2011 ◽

Vol 10 (4) ◽

pp. 912-919 ◽

Cited By ~ 3

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).

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Finite Size Scaling Analysis of Monte Carlo Simulation for the Stipdonk-Hetherington Model in Solid Helium-3–The Phase Transition from Paramagnetic Phase to High Field Phase–

Journal of the Physical Society of Japan ◽

10.1143/jpsj.61.1609 ◽

1992 ◽

Vol 61 (5) ◽

pp. 1609-1614 ◽

Cited By ~ 1

Author(s):

Kazuyuki Matsumoto ◽

Yoshikazu Abe ◽

Anju Sawada

Keyword(s):

Phase Transition ◽

Monte Carlo Simulation ◽

Monte Carlo ◽

High Field ◽

Solid Helium ◽

Finite Size ◽

Scaling Analysis ◽

Finite Size Scaling ◽

Field Phase ◽

Helium 3

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Testing a Fourier-accelerated hybrid Monte Carlo algorithm

Physics Letters B ◽

10.1016/s0370-2693(02)01217-0 ◽

2002 ◽

Vol 528 (3-4) ◽

pp. 301-305 ◽

Cited By ~ 14

Author(s):

Simon Catterall ◽

Sergey Karamov

Keyword(s):

Monte Carlo ◽

Monte Carlo Algorithm ◽

Hybrid Monte Carlo

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Critical phenomena without “hyper scaling”: How is the finite-size scaling analysis of Monte Carlo data affected?

Physics Procedia ◽

10.1016/j.phpro.2010.09.041 ◽

2010 ◽

Vol 7 ◽

pp. 29-33 ◽

Cited By ~ 1

Author(s):

K. Binder

Keyword(s):

Monte Carlo ◽

Critical Phenomena ◽

Finite Size ◽

Scaling Analysis ◽

Finite Size Scaling ◽

Monte Carlo Data ◽

Size Scaling

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COMPARISON OF UPDATE ALGORITHMS FOR PURE GAUGE SU(3)

Modern Physics Letters A ◽

10.1142/s0217732388001641 ◽

1988 ◽

Vol 03 (14) ◽

pp. 1367-1378 ◽

Cited By ~ 36

Author(s):

RAJAN GUPTA ◽

GREGORY W. KILCUP ◽

APOORVA PATEL ◽

STEPHEN R. SHARPE ◽

PHILIPPE DE FORCRAND

Keyword(s):

Monte Carlo ◽

Monte Carlo Algorithm ◽

Hybrid Monte Carlo ◽

Pure Gauge

We show that the overrelaxed algorithm of Creutz and of Brown and Woch is the optimal local update algorithm for simulation of pure gauge SU(3). Our comparison criterion includes computer efficiency and decorrelation times. We also investigate the rate of decorrelation for the Hybrid Monte Carlo algorithm.

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