Novel classical ground state of a many body system in arbitrary dimensions

TL;DR

This paper proves that in a D-dimensional many-body system with two and three body interactions, the classical ground state becomes a linear configuration determined by Hermite polynomial zeros beyond a critical interaction strength.

Contribution

It provides an exact proof of the ground state transition to a linear configuration in arbitrary dimensions based on the strength of three-body interactions.

Findings

Ground state becomes a line beyond critical interaction strength

Particle positions are determined by Hermite polynomial zeros

The result applies to systems in arbitrary dimensions

Abstract

The classical ground state of a D- dimensional many body system with two and three body interactions is studied as a function of the strength of the three body interaction. We prove exactly that beyond a critical strength of the three body interaction, the classical ground state of the system is one in which all the particles are on a line. The positions of the particles in this string configuration are uniquely determined by the zeros of the Hermite polynomials.