Computation Statistical Properties of Disordered Spin Systems from the First Principles of Classical Mechanics
Keywords:Disordered system, Heisenberg spin glass, Ergodic ensemble, NP hard problem, , P algorithm
We study the classical 1D spin glasses in the framework of Heisenberg model. Based on the Hamilton equations we obtained the system of recurrence equations, which allows performing node-by-node calculations of a spin-chain. It is shown that the calculations from the first principles of classical mechanics lead to NP hard problem, that however, in the limit of the statistical equilibrium can be calculated by P algorithm. For the partition function of the ensemble a new representation is offered in the form of one-dimensional integral of spin-chains’ energy distribution.
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