The Devil's staircase and harmless staircase. I. Oscillating interactions through elastic strains or other harmonic fields

Abstract

It is shown that elastic strains or other harmonic fields can mediate oscillating indirect interactions if direct interactions are not limited to nearest neighbours. In particular the mean-field approximation of the Ising model with competing interactions can be interpreted at low temperature in terms of walls (or 'solitons') which interact through an oscillating effective potential. As a result the changes of period are found to be first-order transitions. The phase diagram is therefore not a 'Devil's staircase', in agreement with independent results of Fisher and Selke (1980).