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q-state Potts model metastability study using optimized GPU-based Monte Carlo algorithms

Ezequiel E. Ferrero, Juan Pablo De Francesco, Nicolas Wolovick, Sergio A. Cannas
Facultad de Matematica, Astronomia y Fisica, Universidad Nacional de Cordoba, Ciudad Universitaria, 5000 Cordoba, Argentina
arXiv:1101.0876 [cond-mat.stat-mech] (5 Jan 2011)

@article{2011arXiv1101.0876F,

   author={Ferrero}, E.~E. and {De Francesco}, J.~P. and {Wolovick}, N. and {Cannas}, S.~A.},

   title={“{q-state Potts model metastability study using optimized GPU-based Monte Carlo algorithms}”},

   journal={ArXiv e-prints},

   archivePrefix={“arXiv”},

   eprint={1101.0876},

   primaryClass={“cond-mat.stat-mech”},

   keywords={Condensed Matter – Statistical Mechanics, Physics – Computational Physics},

   year={2011},

   month={jan},

   adsurl={http://adsabs.harvard.edu/abs/2011arXiv1101.0876F},

   adsnote={Provided by the SAO/NASAAstrophysics Data System}

}

We implemented a GPU based parallel code to perform Monte Carlo simulations of the two dimensional q-state Potts model. The algorithm is based on a checkerboard update scheme and assigns independent random numbers generators to each thread (one thread per spin). The implementation allows to simulate systems up to ~10^9 spins with an average time per spin flip of 0.147ns on the fastest GPU card tested, representing a speedup up to 155x, compared with an optimized serial code running on a standard CPU. The possibility of performing high speed simulations at large enough system sizes allowed us to provide a positive numerical evidence about the existence of metastability on very large systems based on Binder’s criterion, namely, on the existence or not of specific heat singularities at spinodal temperatures different of the transition one.
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