Melting as the transition to a curved space

Abstract

It is shown that a crystal lattice at high enough temperatures is unstable with respect to the transition into a space of constant negative curvature. The instability is associated with melting of the crystal. The curvature is proportional to the density of disclinations in the real physical space. The temperature of melting is found as the functional of the pair inter-atomic potential. In a good approximation this temperature depends only on the second derivative of the interatomic potential at the point of the maximum, i.e. on the volume bulk module. The Lindemann ratio is expressed through the first zero of the interatomic potential.