Maizelis Z. Non-additive statistical properties of one-dimensional Ising spin chains with long-range interactions

A method for calculating the statistical properties of one-dimensional mesoscopical systems, based on their statistical matching with many-step Markov chains, is proposed. This method is used for the analysis of the properties of Ising spin chains fragments, taking into account long-range interactions in the chain. The chains considered are in the state of thermodynamic equilibrium. For every spin chain a Markov chain possessing the same statistical properties, is found. A method for calculating the correlation functions of different orders of many-step Markov chain is proposed. This allows analyzing its arbitrary statistical characteristics. The proved equivalence between Markov and Ising spin chains is used for the analysis of magnetic properties of the fragments of spin chain. Non-extensive total and internal energy and entropy of the fragment of Ising spin chain is found. The results obtained pass to the well-known results for the case of taking into account the nearest-neighbors interaction only.