POSSIBLE DISORDERED GROUND-STATES FOR LAYERED SOLIDS AND THEIR DIFFRACTION PATTERNS

It has recently been shown, assuming only certain (physical) symmetrie s of the Hamiltonian, that one-dimensional Ising problems can have deg enerate, disordered ground states (GS's). This result is of interest s ince it implies a weak violation of the third law of thermodynamics. T he ground-state disorder is, however, of a special kind, consisting of arbitrary mixtures of a short-period structure and its symmetry-degen erate partner or partners. In this study, we address the question of h ow this constrained disorder may appear in an experimentally accessibl e signal, namely, the diffraction pattern. To calculate the latter, we assume (as is commonly done with known polytypes) that the Ising Hami ltonian represents the energetics of stacking of close-packed layers o f some hypothetical polytypic material. We then calculate the diffract ion patterns along the stacking direction for the various possible kin ds of disordered GS's. We find that some disordered GS's give diffract ion patterns which are only weakly distinguished from their periodic c ounterparts, while in others the long-ranged correlations among the la yers is destroyed by the disorder, giving a diffraction spectrum which is purely continuous.