title: Annealed Ising model with site dilution on self-similar structures.
abstract: We consider an Ising model on the triangular Apollonian network (AN), with a thermalized distribution of vacant sites. The statistical problem is formulated in a grand canonical ensemble, in terms of the temperature T and a chemical potential μ associated with the concentration of active magnetic sites. We use a well-known transfer-matrix method, with a number of adaptations, to write recursion relations between successive generations of this hierarchical structure. We also investigate the analogous model on the diamond hierarchical lattice (DHL). From the numerical analysis of the recursion relations, we obtain various thermodynamic quantities. In the μ→∞ limit, we reproduce the results for the uniform models: in the AN, the system is magnetically ordered at all temperatures, while in the DHL there is a ferromagnetic-paramagnetic transition at a finite value of T. Magnetic ordering, however, is shown to disappear for sufficiently large negative values of the chemical potential.
authors.affiliation: Instituto de Física, Universidade Federal da Bahia, 40210-210 Salvador, Brazil.
authors.forename: V S T
authors.initials: VS
authors.lastname: Silva
authors.affiliation: Instituto de Física, Universidade Federal da Bahia, 40210-210 Salvador, Brazil.
authors.forename: R F S
authors.initials: RF
authors.lastname: Andrade
authors.affiliation: Instituto de Física, Universidade de São Paulo, Caixa Postal 66318, 05315-970 São Paulo, São Paulo, Brazil.
authors.forename: S R
authors.initials: SR
authors.lastname: Salinas