Phase transitions in fractal porous media

Abstract

Phase transitions in fractal porous media are studied using a spin model with correlated dilution parametrized by a microscopic porosity p and a Hausdorf dimension D. For D>${\mathit{D}}_{\mathrm{crit}}$ ther is a percolation transition for the pore space at some ${\mathit{p}}_{\mathit{c}}$ and, for p>${\mathit{p}}_{\mathit{c}}$, the spins in the pore space exhibit two critical points at the bulk transition temperature, ${\mathit{T}}_{\mathit{c}0}$ and at ${\mathit{T}}_{\mathit{c}}$<${\mathit{T}}_{\mathit{c}0}$. The correlation-length exponent at ${\mathit{T}}_{\mathit{c}}$ is larger than in the corresponding pure system. The qualitative features of the model resemble those of the superfluid transition in aerogel.