Multiple Ising Spins Coupled to 2d Quantum Gravity

TL;DR

This paper investigates a model where multiple Ising spins interact with 2D quantum gravity, analyzing the behavior of the system in various limits and identifying dominant graph structures.

Contribution

It introduces a solvable truncated model for multiple Ising spins coupled to 2D quantum gravity and explores the critical behavior and phase transitions.

Findings

Dominant graph structures identified in the large p limit.

Exact solution of the truncated model for small beta.

Bound derived for the critical coupling constant beta_c.

Abstract

We study a model in which p independent Ising spins are coupled to 2d quantum gravity (in the form of dynamical planar phi-cubed graphs). Consideration is given to the p tends to infinity limit in which the partition function becomes dominated by certain graphs; we identify most of these graphs. A truncated model is solved exactly providing information about the behaviour of the full model in the limit of small beta. Finally, we derive a bound for the critical value of the coupling constant, beta_c and examine the magnetization transition in the limit p tends to zero.