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CivilComp Proceedings
ISSN 17593433 CCP: 95
PROCEEDINGS OF THE SECOND INTERNATIONAL CONFERENCE ON PARALLEL, DISTRIBUTED, GRID AND CLOUD COMPUTING FOR ENGINEERING Edited by:
Paper 72
Parallel Wolff Cluster Algorithm for nComponent Vector Spin Models J. Kaupuzs^{1,2}, R.V.N. Melnik^{3} and J. Rimšans^{1,2}
^{1}Institute of Mathematics and Computer Science, University of Latvia, Riga, Latvia
, "Parallel Wolff Cluster Algorithm for nComponent Vector Spin Models", in , (Editors), "Proceedings of the Second International Conference on Parallel, Distributed, Grid and Cloud Computing for Engineering", CivilComp Press, Stirlingshire, UK, Paper 72, 2011. doi:10.4203/ccp.95.72
Keywords: parallel cluster algorithms, lattice spin models, Monte Carlo simulations, Goldstone mode singularities, correlation functions, power law.
Summary
external field. Then we consider a modified Wolff algorithm,
which can be applied to spin systems in the presence of an external field.
A parallel Open MP version of the standard Wolff algorithm for the threedimensional Ising model has been developed
earlier [2]. Here we generalize this parallel algorithm for spin models, often called nvector
models or O(n) models, where spins are ncomponent vectors. The Ising model is included here as a particular case
of n=1. Further on, we elaborate a parallel version of the modified Wolff algorithm in order to simulate
O(n) models below the critical temperature in the presence of the external field and to study the
Goldstone mode effects. A parallel FORTRAN code for this algorithm has been developed and tested,
allowing us to speed up the simulation (up to 3 times on 4 processors),
as well as to treat larger lattices due to greater operative (shared)
memory available. Using this code, we have simulated the ncomponent vector model
for n=2,4,10 and have analysed the Goldstone mode singularities for the transverse and the longitudinal
Fouriertransformed twopoint correlation functions.
The simulation results for n=10 at several linear lattices sizes L=192,256,384 and small
values of the external field h=0.000875,0.0004375,0.00021875 are discussed in some detail
to test the theoretical predictions for the powerlaw Goldstone mode singularities of the correlation functions.
The results obtained provide good numerical evidence for the theoretically expected powerlaw
divergence of the transverse correlation function at small wave vectors. We have found that by fitting the Monte Carlo
data that this divergence is described by the exponent about 1.97 with an uncertainty of order 0.01 in this value.
The longitudinal correlation function is analysed, as well. Generally,
the simulation results show that the transverse
correlation function has remarkably smaller finitesize and finiteh effects, as well as a better
powerlaw scaling in certain finite range of the wave vector magnitude k,
as compared to the longitudinal correlation function.
References
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