Phase transitions in regularly diluted 2D Ising models with a complicated inherent structure of a lattice cell

We analyze the critical point and study the nonuniversal peculiarities occuring in the temperature dependence of the specific heat for a sequence of the exactly solvable highly decorated two-dimensional triangular-type ferromagnetic Ising models with a complicated (fractal-type) inherent structure of elementary cell. The lattices are indexed by the decoration parameter n = 0, 1, 2, 3,…. The elementary cell for the n-lattice is the nth order lattice approximation of the Sierpiński gasket fractal. At any finite n there is the second order phase transition indicated by the logarithmic singularity in the specific heat. The critical temperature decreases as 4(ln 4n)−1 with increasing decoration, the specific-heat critical amplitude vanishes as 3−n(n ln n)2 as n→∞. The basic nonuniversal features observable in the specific heat at strong decoration are the anomalous narrowing of the critical interval and the appearance of a rounded peak above the true Tc point. These effects are closely related and can both be explained by the above-Tc local ordering in the local lattice inhomogeneities. The mechanism of the above-Tc local ordering is analyzed. The models under discussion can as well be interpreted as the regular bond diluted 2D Ising ferromagnets with a hierarchy of the nonmagnetic holes at different scales and varying dilution. A comparative discussion on the properties of the regularly and randomly diluted 2D Ising ferromagnets is given.