New algorithm for simulation of 3D classical spin glasses under the influence of external electromagnetic fields

We study statistical properties of 3D classical spin glass under the influence of external fields. It is proved that in the framework of the nearest-neighboring model, 3D spin-glass problem at performing of Birkhoff's ergodic hypothesis regarding the orientations of spins in 3D space can be reduced to the problem of disordered 1D spatial spin-chains (SSC) ensemble, where each spin chain interacts with a random environment. The 1D SSC is defined as a periodic 1D lattice, where spins in nodes are randomly oriented in 3D space, in addition, they all interact with each other randomly. For minimization of the Hamiltonian in an arbitrary node of 1D lattice the recurrent equations and corresponding Sylvester's criterion are obtained, which allow one to find the energy local minimum. On the basis of these equations, the high-performance parallel algorithm is developed, which allows one to calculate all statistical parameters of 3D spin glass, including distribution of a constant of spin-spin interaction, from the first principles of the classical mechanics.