Maximally even sets and the devil’s-staircase phase diagram for the one-dimensional Ising antiferromagnet with arbitrary-range interaction

Abstract

By extending the formalism of maximally even sets to the one-dimensional antiferromagnetic Ising model with arbitrary-range interaction in an applied magnetic field it is shown that the system exhibits a devil’s-staircase magnetic phase diagram. A “generalized” similarity dimension (a generalization for nonuniform fractals) of the phase diagram is calculated and compared to previous results. It is shown that previous estimates of the dimension of the phase diagram for this system differs from this “generalized” similarity dimension.