Multifractal analysis of first-order phase transitions in an Ising system with four-spin interactions

The multifractal formalism is applied for investigating probability measure s of energy levels of an Ising model with four-spin interactions on finite- size hexagonal lattices. The Holder exponent characterizing singularities o f these measures is determined as a function of the temperature variable an d the ratio of the strength of four-spin interactions to the strength of tw o-spin couplings. It is shown that for the variable values at which the sys tem reveals the existence of a precursor of the first-order phase transitio n, the maximal Holder exponent, associated with the energy region of the mo st concentrated probability measure, possesses a minimum. which is nondiffe rentiable with respect to temperature. (C) 2000 Elsevier Science B.V. All r ights reserved.