2019/07/10 by Helen Au-Yang, Jacques H. H. Perk, Au-Yang, Helen +1
Mathematics · Physics and Astronomy · #FOS: Physical sciences #Mathematical Physics (math-ph) #Random Matrices and Applications #Statistical Mechanics (cond-mat.stat-mech) #Stochastic processes and statistical mechanics #Theoretical and Computational Physics #cond-mat.stat-mech #math-ph #math.MP
paper · pdf · doi:10.48550/arxiv.1907.04748
34 pages, 2 figures, third paper after arXiv:1806.00873 and arXiv:1808.07525. Plan is to submit them together after some corrections and adding some further references
arxiv created 2019/07/10 · openalex publication_date 2019/07/10 · arxiv updated 2019/07/11 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
In our previous works on infinite horizontal Ising strips of width m alternating with layers of strings of Ising chains of length n, we found the surprising result that the specific heats are not much different for different values of N, the separation of the strings. For this reason, we study here for N=1 the spin-spin correlation in the central row of each strip, and also the central row of a strings layer. We show that these can be written as a Toeplitz determinants. Their generating functions are ratios of two polynomials, which in the limit of infinite vertical size become square roots of polynomials whose degrees are m+1 where m is the size of the strips. We find the asymptotic behaviors near the critical temperature to be two-dimensional Ising-like. But in regions not very close to criticality the behavior may be different for different m and n. Finally, in the appendix we shall present results for generating functions in more general models.