On Modeling of Statistical Properties of Classical 3D Spin Glasses

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Abstract


The 3D spin glass is represented as an ensemble of disordered 1D spatial spin-chains (SSC) where interactions are random between spin-chains. It is proved that at the limit of Birkhoffs ergodic hypothesis performance 3D spin glasses can be generated by Hamiltonian of disordered 1D SSC with random environment. Disordered 1D SSC is defined on a regular lattice where one randomly oriented spin is put on each node of lattice. Also it is supposed that each spin randomly interacts with six nearest-neighboring spins (two spins on lattice and four in the environment). The recurrent transcendental equations are obtained on the nodes of spin-chain lattice. These equations combined with the Silvester conditions allow step by step construct spin-chain in the ground state of energy where all spins are in minimal energy of classical Hamiltonian. On the basis of these equations an original high-performance parallel algorithm is developed for 3D spin glasses simulation.

A S Gevorkyan

Institute for Informatics and Automation Problems

Email: g_ashot@sci.am
НАН Армении; Институт информатики и проблем автоматики; Institute for Informatics and Automation Problems

H G Abajyan

Joint Institute for Nuclear Research

Email: habajyan@ipia.sci.am
Лаборатория информационных технологий; Объединённый институт ядерных исследований; Joint Institute for Nuclear Research

E A Ayryan

Institute for Informatics and Automation Problems

Email: ayrjan@jinr.ru
НАН Армении; Институт информатики и проблем автоматики; Institute for Informatics and Automation Problems

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Copyright (c) 2011 Геворкян А.С., Абаджян А.Г., Aйрян Э.А.

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