2007/07/26 by Nasir Ganikhodjaev, Ganikhodjaev, Nasir, Fatimah Abdul Razak +1 · 1 citation
Mathematics · Physics and Astronomy · #82B20 #FOS: Mathematics #FOS: Physical sciences #Markov Chains and Monte Carlo Methods #Mathematical Physics (math-ph) #Probability (math.PR) #Spectral Theory in Mathematical Physics #Theoretical and Computational Physics #math-ph #math.MP #math.PR #msc:82B20
paper · pdf · doi:10.48550/arxiv.0707.3848
14 pages
arxiv created 2007/07/26 · openalex publication_date 2007/07/26 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
In this paper, correlation inequalities which have been considered on Ising model are extended to q-Potts model. It is considered on generalized Potts model with interaction of any number of spins. We replace the set of spin values F=\1,2,..., q\ by the centered set F=\-(q-1)/2,-(q-3)/2,... ,(q-3)/2,(q-1)/2\. Let N be the subset of one-dimensional lattice with n vertices, \g=(\s1,\s2,...,\sn):N → Fc be a configuration where (\si)_\g is the number which appears as the ith spin (component) in \g and \si be a random variable whose value at \g is (\si)_\g. Define \sR=∏i ∈ R\si for any list R where any i ∈ R implies that i ∈ N. We first prove that <\sR > ≥ 0 then we prove that for any two lists R and S, we have <\sR \sS >- < \sR > < \sS > ≥ 0.