Lee-Yang Zeros of the antiferromagnetic Ising Model

Bencs, Ferenc and Buys, P. and Guerini, L. and Peters, H. (2019) Lee-Yang Zeros of the antiferromagnetic Ising Model. Annales de l'Institut Henri Poincare (D) Combinatorics, Physics and their Interactions. ISSN 2308-5827

Preview

Text 1907.07479v1.pdf Download (2MB) | Preview

Abstract

We investigate the location of zeros for the partition function of the anti-ferromagnetic Ising Model, focusing on the zeros lying on the unit circle. We give a precise characterization for the class of rooted Cayley trees, showing that the zeros are nowhere dense on the most interesting circular arcs. In contrast, we prove that when considering all graphs with a given degree bound, the zeros are dense in a circular sub-arc, implying that Cayley trees are in this sense not extremal. The proofs rely on describing the rational dynamical systems arising when considering ratios of partition functions on recursively defined trees.

Actions (login required)

Edit Item