Geometrically induced long-range orientational order in a solid

A stochastic model of a solid that, through the action of random factors, has lost translational order but preserves the topological structure of short-range interatomic bonds characteristic of a crystal is studied. It is shown that in such a body there must be a long-range orientational order. To this end, a multidimensional analog of the ergodic theorem for a regular lattice subject to random deformation with spatially homogeneous distribution is proved.