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.

AN APPLICATION OF A CLUSTER MONTE CARLO METHOD TO THE HEISENBERG MODEL

1993 ◽  
Vol 04 (05) ◽  
pp. 1041-1048 ◽  
Author(s):  
CESARE CHICCOLI ◽  
PAOLO PASINI ◽  
FRANCO SEMERIA ◽  
CLAUDIO ZANNONI
Keyword(s):  
Monte Carlo ◽  
Monte Carlo Method ◽  
Boundary Conditions ◽  
Maximum Entropy ◽  
Heisenberg Model ◽  
Classical Heisenberg Model ◽  
Self Consistent ◽  
Cluster Monte Carlo

A Monte Carlo method with boundary conditions of a self-consistent maximum entropy type has been applied to the classical Heisenberg model.

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.

CRITICAL DYNAMICS IN THE 3D SPIN-1/2 HEISENBERG MODEL: A DECOUPLED CELL MONTE CARLO STUDY

1996 ◽  
Vol 07 (03) ◽  
pp. 441-447 ◽  
Author(s):  
CYNTHIA J. SISSON
Keyword(s):  
Monte Carlo ◽  
Quantum Monte Carlo ◽  
Heisenberg Model ◽  
Three Dimensional ◽  
Monte Carlo Study ◽  
System Size ◽  
Classical Heisenberg Model ◽  
Monte Carlo Studies ◽  
Theoretical Predictions ◽  
Good Agreement

The three-dimensional spin-1/2 Heisenberg model on a simple cubic lattice is studied for ferromagnetic and antiferromagnetic interactions using the Decoupled Cell Method for quantum Monte Carlo. Results for the relaxation time τL are determined for both ferromagnetic and antiferromagnetic systems and found to be similar to those found for the classical (s → ∞) Heisenberg model. The scaling of τL with system size is used to extract the dynamical critical exponent z for the two systems. The values of z = 1.98 ± 0.12 for the ferromagnet and z = 1.94 ± 0.09 for the antiferromagnet are in good agreement with theoretical predictions and previous Monte Carlo studies of the classical Heisenberg model.

Non-Equilibrium Critical Relaxation of Heisenberg Ferromagnets with Long-Range Correlated Defects

2012 ◽  
Vol 190 ◽  
pp. 39-42
Author(s):  
M. Medvedeva ◽  
Pavel V. Prudnikov
Keyword(s):  
Monte Carlo ◽  
Monte Carlo Simulations ◽  
Critical Behavior ◽  
Critical Exponents ◽  
Heisenberg Model ◽  
Three Dimensional ◽  
Initial State ◽  
Short Time ◽  
Theoretic Description ◽  
Good Agreement

The dynamic critical behavior of the three-dimensional Heisenberg model with longrangecorrelated disorder was studied by using short-time Monte Carlo simulations at criticality.The static and dynamic critical exponents are determined. The simulation was performed fromordered initial state. The obtained values of the exponents are in a good agreement with resultsof the field-theoretic description of the critical behavior of this model in the two-loopapproximation.

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