Dynamically Triangulated Ising Spins in Flat Space

TL;DR

This paper introduces a model of Ising spins moving randomly on a flat surface with hard core repulsion, revealing multicritical behavior and tricritical points consistent with random geometry models.

Contribution

It presents a novel dynamic flat-space Ising model with hard core interactions, connecting it to known random geometry solutions and analyzing its phase transitions.

Findings

Model exhibits multicritical behavior with first and second order transitions.

Thermal and magnetic exponents match the two-matrix model solution.

Identifies a tricritical point consistent with fluctuating geometry theories.

Abstract

A model describing Ising spins with short range interactions moving randomly in a plane is considered. In the presence of a hard core repulsion, which prevents the Ising spins from overlapping, the model is analogous to a dynamically triangulated Ising model with spins constrained to move on a flat surface. It is found that as a function of coupling strength and hard core repulsion the model exhibits multicritical behavior, with first and second order transition lines terminating at a tricritical point. The thermal and magnetic exponents computed at the tricritical point are consistent with the exact two-matrix model solution of the random Ising model, introduced previously to describe the effects of fluctuating geometries.