Novel Classical Ground State of a Many Body System in Arbitrary Dimensions

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.