A polymer gas on a random surface

TL;DR

This paper models a polymer gas on a random surface using quantum gravity, deriving its free energy and equation of state, revealing that higher-order virial coefficients are zero, indicating simplified interactions.

Contribution

It introduces a novel approach linking polymer configurations to random surfaces with quantum gravity, providing exact calculations of thermodynamic properties.

Findings

Derived the free energy of the polymer gas.

Established the equation of state for the system.

Found all virial coefficients beyond the second vanish.

Abstract

Using the observation that configurations of N polymers with hard core interactions on a closed random surface correspond to random surfaces with N boundary components we calculate the free energy of a gas of polymers interacting with fully quantized two-dimensional gravity. We derive the equation of state for the polymer gas and find that all the virial coefficients beyond the second one vanish identically.