DILUTED POTTS-MODEL ON DIAMOND-TYPE HIERARCHICAL LATTICES

The bond-diluted q-state Potts model situated on a fractal family of d iamond-type hierarchical lattices is investigated with the renormaliza tion-group method. We find that in the ferromagnetic-interaction case there is a borderline value q(t) on the lattice with D(f) less-than-or -equal-to 2. When q > q(t) there is a crossover to a diluted fixed poi nt (critical region). However, two borderline values q(t1) and q(t2) ( q(t1) < q(t2)) appear on the lattices with D(f) > 2. In the region q(t 1) < q < q(t2), the two diluted fixed points coexist, one is critical and another is tricritical. These fixed points merge and annihilate at q(t1). As q increases from q(t1), the tricritical point approaches an d meets with the pure fixed point at q(t2). The critical behavior of t he system is governed by the critical diluted fixed point when the con centration of occupied bonds is below its tricritical value, otherwise it is governed by the pure fixed point. This feature implies that the concentration of occupied bonds is relevant to the critical propertie s of the system. We also discuss the antiferromagnetic case and our re sults show that the critical properties of the system are unchanged by dilution.