A new parallel algorithm for simulation of spin glasses on scales of space-time periods of external fields with consideration of relaxation effects

We have investigated the statistical properties of an ensemble of disordered 1D spatial spin chains (SSCs) of finite length, placed in an external field, with consideration of relaxation effects. The short-range interaction complex-classical Hamiltonian was first used for solving this problem. A system of recurrent equations is obtained on the nodes of the spin-chain lattice. An efficient mathematical algorithm is developed on the basis of these equations with consideration of the advanced Sylvester conditions which allow step by step construct a huge number of stable spin chains in parallel. The distribution functions of different parameters of spin-glass system are constructed from the first principles of the complex classical mechanics by analyzing the calculation results of the 1D SSCs ensemble. It is shown that the behavior of the parameter distributions is quite different depending on the external fields. The energy ensembles and constants of spin-spin interactions are changed smoothly depending on the external field in the limit of statistical equilibrium, while some of them such as the mean value of polarizations of ensemble and parameters of its orderings are frustrated. We have also studied some critical properties of the ensemble of such catastrophes in the Clausius-Mossotti equation depending on the value of the external field. We have shown that the generalized complex-classical approach excludes these catastrophes allowing one to organize continuous parallel computing on the whole region of values of the external field including critical points. A new representation of the partition function based on these investigations is suggested. As opposed to usual definition, this function is a complex one and its derivatives are everywhere defined, including critical points