The analytic structure of lattice models – Why can't we solve most models?

Pramana

Anthony J Guttmann1¹ 

[1] Department of Mathematics and Statistics, University of Melbourne, Vic. 3010, Australia$$

关键词: Solvability;    differentiably finite;    bond animal;    Ising model;    susceptibility;    self-avoiding walks;    self-avoiding polygons.;   

DOI  :  

学科分类：物理（综合）

来源: Indian Academy of Sciences

【 摘 要 】

We investigate the solvability of a variety of well-known problems in lattice statistical mechanics. We provide a new numerical procedure which enables one to conjecture whether the solution falls into a class of functions called differentiably finite functions. Almost all solved problems fall into this class. The fact that one can conjecture whether a given problem is or is not 𝐷-finite then informs one as to whether the solution is likely to be tractable or not. We also show how, for certain problems, it is possible to prove that the solutions are not 𝐷-finite, based on the work of Rechnitzer [1–3].

【 授权许可】

Unknown