A Two Term Truncation of the Multiple Ising Model Coupled to 2d Gravity

TL;DR

This paper introduces an exactly solvable two-term truncated model of multiple Ising spins coupled to 2D gravity, revealing a third-order phase transition and estimating the critical number of spins for a branched polymer phase.

Contribution

It presents a novel solvable truncation of the Ising model coupled to 2D gravity, analyzing phase transitions and estimating critical parameters for the emergence of branched polymer phases.

Findings

Identifies a third-order phase transition between gravity and tree-like phases.

Provides an estimate for the number of spins where branched polymer phase appears.

Determines the critical line with gamma=1/3 in the model.

Abstract

We consider a model of p independent Ising spins on a dynamical planar phi-cubed graph. Truncating the free energy to two terms yields an exactly solvable model that has a third order phase transition from a pure gravity region (gamma=-1/2) to a tree-like region (gamma=1/2), with gamma=1/3 on the critical line. We are able to make an order of magnitude estimate of the value of p above which there exists a branched polymer (ie tree-like) phase in the full model, that is, p is approximately 13-23, which corresponds to a central charge c of about 6-12.