Critical region for an Ising model coupled to causal dynamical triangulations

TL;DR

This paper analyzes the phase transition region of the annealed Ising model coupled to 2D causal dynamical triangulations using FK representation, identifying critical and subcritical regions and improving free energy estimates.

Contribution

It extends previous results by precisely delineating the critical region and improving subcritical bounds for the model.

Findings

Identified a region where the model has a unique infinite-volume Gibbs measure.

Determined a region where the finite-volume Gibbs measure does not have a weak limit.

Provided a better approximation of the free energy.

Abstract

This paper extends results obtained by [15] for the annealed Ising model coupled to two-dimensional causal dynamical triangulations. We employ the Fortuin-Kasteleyn (FK) representation in order to determine a region in the quadrant of parameters $\beta,\mu>0$ where the critical curve for the annealed model is possibly located. This is done by outlining a region where the model has a unique infinite-volume Gibbs measure, and a region where the finite-volume Gibbs measure does not have weak limit (in fact, does not exist if the volume is large enough). We also improve the region of subcritical behaviour of the model, and provide a better approximation of the free energy.