2018/06/03 by Helen Au-Yang, Jacques H. H. Perk, Au-Yang, Helen +1 · 1 citation
Physics and Astronomy · #Complex Network Analysis Techniques #FOS: Physical sciences #Opinion Dynamics and Social Influence #Statistical Mechanics (cond-mat.stat-mech) #Theoretical and Computational Physics #cond-mat.stat-mech
paper · pdf · doi:10.48550/arxiv.1806.00873
LaTeX, 16 pages, 7 figures (13 pdf files), first part with results, second part with formal details to follow
arxiv created 2018/06/03 · openalex publication_date 2018/06/03 · arxiv updated 2018/06/05 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
In order to investigate the effects of connectivity and proximity in the specific heat, a special class of exactly solvable planar layered Ising models has been studied in the thermodynamic limit. The Ising models consist of repeated uniform horizontal strips of width m connected by sequences of vertical strings of length n mutually separated by distance N, with N=1,2 and 3. We find that the critical temperature Tc(N,m,n), arising from the collective effects, decreases as n and N increase, and increases as m increases, as it should be. The amplitude A(N,m,n) of the logarithmic divergence at the bulk critical temperature Tc(N,m,n) becomes smaller as n and m increase. A rounded peak, with size of order ln m and signifying the one-dimensional behavior of strips of finite width m, appears when n is large enough. The appearance of these rounded peaks does not depend on m as much, but depends rather more on N and n, which is rather perplexing. Moreover, for fixed m and n, the specific heats are not much different for different N. This is a most surprising result. For N=1, the spin-spin correlation in the center row of each strip can be written as a Toeplitz determinant with a generating function which is much more complicated than in Onsager's Ising model. The spontaneous magnetization in that row can be calculated numerically and the spin-spin correlation is shown to have two-dimensional Ising behavior.