Bounds on the critical line via transfer matrix methods for an Ising model coupled to causal dynamical triangulations

TL;DR

This paper develops a transfer matrix approach to analyze the Ising model coupled with causal dynamical triangulations, identifying parameter regions where the free energy converges and studying the model's asymptotic behavior.

Contribution

It introduces a novel transfer matrix formalism for the coupled Ising and dynamical triangulations model and applies Krein-Rutman theory to analyze its properties.

Findings

Identifies parameter regions with convergent free energy.

Analyzes asymptotic properties of the partition function.

Provides bounds on the critical line for the model.

Abstract

We introduce a transfer matrix formalism for the (annealed) Ising model coupled to two-dimensional causal dynamical triangulations. Using the Krein-Rutman theory of positivity preserving operators we study several properties of the emerging transfer matrix. In particular, we determine regions in the quadrant of parameters beta, mu >0 where the infinite-volume free energy converges, yielding results on the convergence and asymptotic properties of the partition function and the Gibbs measure.