The phase diagram of an Ising model on a polymerized random surface

TL;DR

This paper explores a random surface model combining Ising spins and outgrowths, revealing a triple point where different gravity phases and a branched polymer phase coexist, characterized by a specific susceptibility exponent.

Contribution

It introduces a novel random surface model with outgrowths and identifies a triple point with a specific susceptibility exponent, connecting different gravity phases.

Findings

Identified a triple point with susceptibility exponent 1/4.

Established the coexistence of magnetized, nonmagnetized, and branched polymer phases.

Demonstrated fine-tuning of parameters leads to critical behavior in the model.

Abstract

We construct a random surface model with a string susceptibility exponent one quarter by taking an Ising model on a random surface and introducing an additional degree of freedom which amounts to allowing certain outgrowths on the surfaces. Fine tuning the Ising temperature and the weight factor for outgrowths we find a triple point where the susceptibility exponent is one quarter. At this point magnetized and nonmagnetized gravity phases meet a branched polymer phase.