Critical line of the Ising model on 2-dimensional CDT and its dual

TL;DR

This paper investigates the critical behavior of the Ising model coupled with 2D causal dynamical triangulations, establishing the critical line, analyzing its properties, and exploring duality relations.

Contribution

It introduces the analytical derivation of the critical line for the coupled model and examines its properties and duality relations.

Findings

Existence of the critical line is proven.

Analytical properties and asymptotics of the critical line are derived.

Relations between the model and its dual are explored.

Abstract

In this paper we study the annealed coupling of an Ising model with 2-dimensional causal dynamical triangulation model. After a short review of previous results, we prove the existence of the so-called critical line and derive its analytical properties and asymptotics. In addition, relations between the model and its dual are investigated.