System of recursive equations for the partition functions of 1D models

2009/04/04 by U. A. Rozikov, Rozikov, U. A.
Mathematics · Physics and Astronomy · #37N25 #82B20 #Advanced Topics in Algebra #Algebraic structures and combinatorial models #Dynamical Systems (math.DS) #FOS: Mathematics #FOS: Physical sciences #Markov Chains and Monte Carlo Methods #Mathematical Physics (math-ph) #math-ph #math.DS #math.MP #msc:37N25 #msc:82B20

paper · pdf · doi:10.48550/arxiv.0904.0715

9 pages

arxiv created 2009/04/04 · openalex publication_date 2009/04/04 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In this note we consider several kind of partition functions of one-dimensional models with nearest - neighbor interactions I_n, n∈ Z and spin values ± 1. We derive systems of recursive equations for each kind of such functions. These systems depend on parameters I_n, n∈ Z. Under some conditions on the parameters we describe solutions of the systems of recursive equations.

Citations

• An example of one-dimensional phase transition

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