Multifractality and frustration in an antiferromagnetic Ising model

Multifractal formalism is used to study properties of probability measures supported by energy spectra of a fully frustrated nearest-neighbor Ising model on finite-size triangular lattices. The spectra of singularities of these measures as well as the maximal Holder exponent are shown to display a strong asymmetry under the change of the sign of the interaction parameter. Demonstrated is also some similarity between the temperature dependence of this exponent in cases of the antiferromagnetic triangular Ising model and the one-dimensional Ising system. Consequently, the multifractal formalism is proved to be useful for indicating the existence of frustration in lattice systems with discrete energies and for analyzing the influence of frustration on properties of these systems for different temperatures. (C) 1999 Elsevier Science B.V. All rights reserved.