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Asymptotic scaling in the two-dimensional O(3) Nonlinear sigma model: a Monte Carlo study on parallel computers
[摘要]

We investigate the 2d O(3) model with the standard action by Monte Carlo simulation at couplingsβ up to 2.05. We measure the energy density, mass gap and susceptibility of the model, and gather high statistics on lattices of size L ≤ 1024 using the Floating Point Systems T-series vector hypercube and the Thinking Machines Corp.'s Connection Machine 2. Asymptotic scaling does not appear to set in for this action, even at β = 2.10, where the correlation length is 420. We observe a 20% difference between our estimate m/Λ^─_(Ms) = 3.52(6) at this β and the recent exact analytical result . We use the overrelaxationalgorithm interleaved with Metropolis updates and show thatdecorrelationtime scales with the correlation length and the number of overrelaxationstepsper sweep. We determine its effective dynamical critical exponent to bez' = 1.079(10); thus critical slowing down is reducedsignificantly for this local algorithm that is vectorizableandparallelizable.

We also use the cluster Monte Carlo algorithms, which are non-local Monte Carlo update schemes which can greatly increase the efficiency of computer simulations of spin models. The major computational task in these algorithms is connected component labeling, to identify clusters of connected sites on a lattice. We have devised some new SIMD component labeling algorithms, and implemented them on the Connection Machine. We investigate their performance when applied to the cluster update of the two dimensionalIsing spin model.

Finally we use a Monte Carlo Renormalization Group method to directly measure the couplings of block Hamiltonians at different blocking levels. For the usual averaging block transformation we confirm the renormalized trajectory (RT) observed by Okawa. For another improved probabilistic block transformation we find the RT, showing that it is much closer to the Standard Action. We then use this block transformation to obtain the discrete β-function of the model which we compare to the perturbative result. We do not see convergence, except when using a rescaled coupling β_E to effectively resum the series. For the latter case we see agreement for m/ Λ^─_(Ms) at , β = 2.14, 2.26, 2.38 and 2.50. To three loopsm/Λ^─_(Ms) = 3.047(35) at β = 2.50, which is very close to the exact valuem/ Λ^─_(Ms) = 2.943. Our last point at β = 2.62 disagrees with this estimate however.

[发布日期]  [发布机构] University:California Institute of Technology;Department:Physics, Mathematics and Astronomy
[效力级别]  [学科分类] 
[关键词] Physics [时效性] 
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