Effects of Pore Walls and Randomness on Phase Transitions in Porous Media

We study spin models within the mean field approximation to elucidate the topology of the phase diagrams of systems modeling the liquid-vapor transition and the separation of He$^3$--He$^4$ mixtures in periodic porous media. These topologies are found to be identical to those of the corresponding random field and random anisotropy spin systems with a bimodal distribution of the randomness. Our results suggest that the presence of walls (periodic or otherwise) are a key factor determining the nature of the phase diagram in porous media.