A Calogero-Sutherland Type Model For Branched Polymers

TL;DR

This paper introduces a Calogero-Sutherland type model with anharmonic interactions that maps to matrix models for branched polymers, pure gravity, and phase transitions, revealing deep connections between these physical systems.

Contribution

It develops a novel Calogero-Sutherland type model with anharmonic interactions that captures the behavior of branched polymers and related phase transitions.

Findings

Model maps to matrix models for branched polymers

Modifications connect to pure gravity phase

Transitions between soap bubble and branched polymer phases

Abstract

We show that a Calogero-Sutherland type model with anharmonic interactions of fourth and sixth orders leads to the matrix model corresponding to the branched polymers. We also show that by suitably modifying this model one can also obtain N-particle problems which are connected to matrix models corresponding to the pure gravity phase as well as corresponding to the transition point between the soap bubble and the branched polymer phase.