Random Ising Spins in Two Dimensions - A Flat Space Realization of the KPZ Exponents

TL;DR

This paper introduces a 2D model of Ising spins with short-range interactions and hard core repulsion, demonstrating multicritical behavior and KPZ exponents consistent with fluctuating geometry theories.

Contribution

It presents a flat space realization of KPZ exponents for Ising spins, linking random spin motion with multicritical phenomena and exact solutions of the two-matrix model.

Findings

Exhibits multicritical behavior with first and second order transition lines.

Thermal and magnetic exponents match KPZ values.

Consistent with the exact two-matrix model solution.

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. 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 KPZ values associated with Ising spins, and with the exact two-matrix model solution of the random Ising model, introduced previously to describe the effects of fluctuating geometries.