Ising Model for the Freezing Transition

A spin-1 Ising model incorporating positional order to a standard lattice gas with no attractive interactions is introduced and found to be consistent with all known attributes of the freezing transition of the hard-sphere system. Implementation of attractive interactions in a fairly natural way then allows every aspect of the phase diagram of a simple substance to be reproduced. The \emph{whole} phase behavior of such sort of substances is thus found to sharply manifest the van der Waals picture highlighting the relevance of harsh repulsive forces.Comment: 10 pages, 4 figure

Ising Paradigm in Isobaric Ensembles

We review recent work on Ising-like models with “compressible cells” of fluctuating volume that, as such, are naturally treated in NpT and μpT ensembles. Besides volumetric phenomena, local entropic effects crucially underlie the models. We focus on “compressible cell gases” (CCG), namely, lattice gases with fluctuating cell volumes, and “compressible cell liquids” (CCL) with singly occupied cells and fluctuating cell volumes. CCGs contemplate singular diameters and “Yang–Yang features” predicted by the “complete scaling” formulation of asymmetric fluid criticality, with a specific version incorporating “ice-like” hydrogen bonding further describing the “singularity-free scenario” for the low-temperature unusual thermodynamics of supercooled water. In turn, suitable CCL variants constitute adequate prototypes of water-like liquid–liquid criticality and the freezing transition of a system of hard spheres. On incorporating vacant cells to such two-state CCL variants, one obtains three-state, BEG-like models providing a satisfactory description of water’s “second-critical-point scenario” and the whole phase behavior of a simple substance like argon. Future challenges comprise water’s crystal–fluid phase behavior and metastable states

Temperature, concentration, and frequency dependence of the dielectric constant near the critical point of the binary liquid mixture nitrobenzene-tetradecane

Detailed results are reported for the dielectric constant epsilon as a function of temperature, concentration, and frequency near the upper critical point of the binary liquid mixture nitrobenzene-tetradecane. The data have been analyzed in the context of the recently developed concept of complete scaling. It is shown that the amplitude of the low frequency critical Maxwell-Wagner relaxation (with a relaxation frequency around 10 kHz) along the critical isopleth is consistent with the predictions of a droplet model for the critical fluctuations. The temperature dependence of epsilon in the homogeneous phase can be well described with a combination of a (1-alpha) power law term (with alpha the heat capacity critical exponent) and a linear term in reduced temperature with the Ising value for alpha. For the proper description of the temperature dependence of the difference Delta epsilon between the two coexisting phases below the critical temperature, it turned out that good fits with the Ising value for the order parameter exponent beta required the addition of a corrections-to-scaling contribution or a linear term in reduced temperature. Good fits to the dielectric diameter epsilon(d) require a (1-alpha) power law term, a 2 beta power law term (in the past considered as spurious), and a linear term in reduced temperature, consistent with complete scaling.status: publishe