TITLE:
A New Parallel Algorithm for Simulation of Spin-Glass Systems on Scales of Space-Time Periods of an External Field
AUTHORS:
A. S. Gevorkyan, H. G. Abajyan, H. S. Sukiasyan
KEYWORDS:
Spin-Glass Hamiltonian, Birkhoff Ergodic Hypothesis, Statistic Distributions, Frustration, Fractal, Parallel Algorithm, Numerical Simulation
JOURNAL NAME:
Journal of Modern Physics,
Vol.2 No.6,
June
30,
2011
ABSTRACT: We study the statistical properties of an ensemble of disordered 1D spatial spin-chains (SSCs) of certain length in the external field. On nodes of spin-chain lattice the recurrent equations and corresponding inequal-ity conditions are obtained for calculation of local minimum of a classical Hamiltonian. Using these equa-tions for simulation of a model of 1D spin-glass an original high-performance parallel algorithm is developed. Distributions of different parameters of unperturbed spin-glass are calculated. It is analytically proved and shown by numerical calculations that the distribution of the spin-spin interaction constant in the Heisenberg nearest-neighboring Hamiltonian model as opposed to the widely used Gauss-Edwards-Anderson distribu-tion satisfies the Lévy alpha-stable distribution law which does not have variance. We have studied critical properties of spin-glass depending on the external field amplitude and have shown that even at weak external fields in the system strong frustrations arise. It is shown that frustrations have a fractal character, they are self-similar and do not disappear at decreasing of calculations area scale. After averaging over the fractal structures the mean values of polarizations of the spin-glass on the scales of external field's space-time peri-ods are obtained. Similarly, Edwards-Anderson’s ordering parameter depending on the external field ampli-tude is calculated. It is shown that the mean values of polarizations and the ordering parameter depending on the external field demonstrate phase transitions of first-order.