The Eigenfunctions of the Transfer Operator for the Dyson model in a field
Probability
2025-07-08 v1 Mathematical Physics
Dynamical Systems
math.MP
Abstract
The recent works \cite{EFMV2024} and \cite{JOP2023} have studied the spectral properties of the Dyson model in the absence of an external field. This paper is a continuation of \cite{EFMV2024} and aims to bridge the gap in the literature by investigating the Dyson model in a field.\\ In this paper, we prove that, for high temperatures or strong magnetic fields, there exists a non-negative, integrable (with respect to the unique half-line Gibbs measure) eigenfunction of the transfer operator for the Dyson model if . However, unlike in the zero-magnetic-field case, this eigenfunction is not continuous.
Cite
@article{arxiv.2502.09588,
title = {The Eigenfunctions of the Transfer Operator for the Dyson model in a field},
author = {Mirmukhsin Makhmudov},
journal= {arXiv preprint arXiv:2502.09588},
year = {2025}
}