Ground-state entropy and algebraic order at low temperatures

Abstract

A rescaling argument is applied to systems with a highly degenerate ground state. It is suggested that these systems can exhibit a distinctive low-temperature phase in which correlations decay algebraically with distance. This behaviour seens to be permitted when the spatial dimensionality is sufficiently high, d>or=d_c. In addition, we find at d_c an infinite-order phase transition ( nu = infinity , alpha =- infinity ) occurring at non-zero temperature, and only paramagnetic behaviour at dc. Since our results arise from a one-parameter renormalisation-group viewpoint, they should be seen as suggestive rather than definitive.