# Classical Spin Glasses with Consideration of Relaxation Effects

## Abstract

The complex-classical short-range interaction Hamiltonian is used for the first time for solving spin glasses with consideration of relaxation effects. A system of recurrent equations is obtained on the nodes of the 1D lattice. An efficient mathematical algorithm is developed on the basis of these equations with consideration of extended Sylvester conditions which allows node-by-node construct a huge number of stable spin chains in parallel. As a result of the simulation, distribution functions of different parameters of a spin glass are constructed from the first principles of complex classical mechanics. Also, the critical properties of spin glass such as catastrophes in the Clausius-Mossotti equation are studied depending on the external field. It is shown that the developed approach excludes these catastrophes, which allows to organize continuous parallel computation based on the whole-range values of the external field. A new representation of the partition function is suggested which, opposite to the usual definition, is a complex function with the derivatives defined everywhere, including at critical points.

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