Discrete and Continuous Models and Applied Computational ScienceDiscrete and Continuous Models and Applied Computational Science2658-46702658-7149Peoples' Friendship University of Russia named after Patrice Lumumba (RUDN University)8435On Modeling of Statistical Properties of Classical 3D Spin GlassesGevorkyanA SНАН Армении; Институт информатики и проблем автоматики; Institute for Informatics and Automation Problemsg_ashot@sci.amAbajyanH GЛаборатория информационных технологий; Объединённый институт ядерных исследований; Joint Institute for Nuclear Researchhabajyan@ipia.sci.amAyryanE AНАН Армении; Институт информатики и проблем автоматики; Institute for Informatics and Automation Problemsayrjan@jinr.ruInstitute for Informatics and Automation ProblemsJoint Institute for Nuclear Research150420114839508092016Copyright © 2011,2011The 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.random 3D networks3D regular latticespin glass Hamiltonianergodic hypothesisstatistic distributionsparallel simulation3D случайная сеть3D регулярная решеткагамильтониан спинового стеклаэргодическая гипотезастатистические распределенияпараллельное моделирование