Correlated Random-Chemical-Potential Model for the Phase Transitions of Helium Mixtures in Porous Media

Abstract

A lattice model is constructed for He-He mixtures in porous media, characterized by correlated random chemical-potential differences between isotopes. Sites with high chemical-potential differences form a random connected porous structure, similar to silica strands in aerogel. We find by Monte Carlo simulation that the bulk tricritical phase diagram is replaced: The A line extends to zero temperature, as had been theoretically predicted some time ago, and phase separation occurs within the superAuid phase. These findings and the behavior of the order parameter agree with recent experiments.

Adsorption of a fluid in an aerogel: Integral equation approach

“…Indeed, aerogels display very specific structural properties that may play an important role for fluid adsorption. In the past, this has motivated the development of various lattice models taking into account all or part of the specific features of the aerogel-induced disorder ; the phase transitions of these models have been studied by various methods, both theoretically and by computer simulation [12][13][14][15][16]. The present work relies on the off-lattice version [17] of the model used in Refs.…”

Equilibrium phase transitions in a porous medium

“…When the pore surfaces couple differently to the two components of a phase-separating mixture, it has been argued that one might expect random-field Ising critical phenomena. 8 In the case where a 3 He- 4 He mixture is confined to the interior of an aerogel, recent theories and calculations 9,10 indicate that the point ͑the low-temperature terminus of the secondorder superfluid transition line͒ is moved to zero temperature, causing phase separation to occur inside the superfluid phase. Mounting theoretical evidence indicates that symmetry-breaking phase transitions may be changed from first to second order by the presence of aerogel-like media.…”

Critical behaviors of bond and crystal field dilution Blume–Emery–Griffiths model

“…For instance, Hui and Berker pointed out that symmetry-breaking first-order transitions are converted to continuous transitions and nonsymmetry-breaking firstorder transitions are entirely eliminated in two-dimensional system, while first-order phase transitions disappear only at a finite amount of randomness in three-dimensional system [21]. The BEG model with a random single-ion anisotropy has modeled the critical behavior of 3 He-4 He mixtures in porous media (such as aerogel) [22,23]. Recently, we notice that a more complicated situation in studying the BCM has been considered.…”