Low-temperature properties of a model glass. I. Elastic dipole model

We develop a model to explain the universal low-temperature properties of glasses in the 1<T<10 K temperature range. Our model consists of elastic dipole ‘‘defects’’ which are placed randomly in an elastic continuum. We derive a Hamiltonian for defects interacting via their long-range strain fields. We simulate a system of elastic dipoles placed on a lattice with site dilution, and find local minima of the defect Hamiltonian using Monte Carlo annealing. For a broad range of dilution, the ground states found are disordered. We study various excitations about these ground states. In this paper (I) we determine the barriers to reorientations of the dipoles, and find that these are in quantitative agreement with dielectric-loss data on the orientational glass KBr:KCN. We also compare our results with other recent theories of orientational glasses. In the following paper (II) we study harmonic excitations about the glassy ground states and the effect of these excitations on the low-temperature thermal properties; we compare our results with experimental data on KBr:KCN and vitreous silica.