Dolan, Brian P. (1998) Geometry and thermodynamic fluctuations of the Ising model on a Bethe lattice. Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences, 454 (1978). pp. 2655-2665. ISSN 1364-5021

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Abstract

A metric is introduced on the two–dimensional space of parameters describing the Ising model on a Bethe lattice of co–ordination number q. The geometry associated with this metric is analysed and it is shown that the Gaussian curvature diverges at the critical point. For the special case q = 2 the curvature reduces to an already known result for the one–dimensional Ising model. The Gaussian curvature is also calculated for a general ferromagnet near its critical point, generalizing a previous result for T > Tc. The general expression near a critical point is compared with the specific case of the Bethe lattice and a subtlety, associated with the fact that the specific heat exponent for the Bethe lattice vanishes, is resolved.

Item Type:	Article
Keywords:	Geometry; thermodynamics;; Ising model; Bethe lattice;
Academic Unit:	Faculty of Science and Engineering > Mathematical Physics
Item ID:	10497
Identification Number:	https://doi.org/10.1098/rspa.1998.0274
Depositing User:	Dr. Brian Dolan
Date Deposited:	18 Feb 2019 14:30
Journal or Publication Title:	Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences
Publisher:	The Royal Society
Refereed:	Yes
URI:	https://royalsocietypublishing.org/
Use Licence:	This item is available under a Creative Commons Attribution Non Commercial Share Alike Licence (CC BY-NC-SA). Details of this licence are available here

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