Multifractal magnetization on hierarchical lattices

A new approach is applied to show that the local magnetization of the ferromagnetic Ising model on hierarchical lattices has a multifractal structure at the critical point. Thef() function characterizing its multifractality is presented and discussed for the diamond hierarchical lattice. Distinct exact critical exponents for the average magnetization and for the local magnetization of the deepest sites are found. The average magnetization (as function of the temperature) is also calculated. The critical exponent of the susceptibility is estimated using finite-size scale arguments.