The effect of long range interactions on the stability of classical and quantum solids

Abstract

We generalise the celebrated Peierls' argument to study the stability of a long-range interacting classical solid. Long-range interaction implies that all the atomic oscillators are coupled to each other via a harmonic potential, though the coupling strength decays as a power-law $1/x^α$, where $x$ is the distance between the oscillators. We show that for the range parameter $α<2$, the long-range interaction dominates and the one-dimensional system retains a crystalline order even at a finite temperature whereas for $α\geq2$, the long-range crystalline order vanishes even at an infinitesimally small temperature. We also study the effect of quantum fluctuations on the melting behaviour of a one-dimensional solid at T=0, extending Peierls' arguments to the case of quantum oscillators.

7 pages REVTEX (including 1 ps figure)