Correlations in classical ground states (Q1095515)

The author gives a purely mathematical treatment of the problem of spatial symmetry in low-temperature crystals where the energy ground states tend to be periodic. The author states to have essentially solved the problem for one-dimensional models in previous papers. In this paper the problem is treated for two- and three-dimensional models. It is shown that energy ground states here tend to have a homogeneity property at least in an average sense, whereby ``homogeneous'' is taken to mean that the configuration is essentially identical (statistically) in any two congruent regions much larger than the period. No physical or technical applications are given.