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

The multifractal formalism is applied for investigating probability measures of energy levels of an Ising model with four-spin interactions on finite-size hexagonal lattices. The Hölder exponent characterizing singularities of these measures is determined as a function of the temperature variable and the ratio of the strength of four-spin interactions to the strength of two-spin couplings. It is shown that for the variable values at which the system reveals the existence of a precursor of the first-order phase transition, the maximal Hölder exponent, associated with the energy region of the most concentrated probability measure, possesses a minimum, which is nondifferentiable with respect to temperature.