Water’s two-critical-point scenario in the Ising paradigm

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.

Ising model for the freezing transition

We introduce a three-state Ising model with entropy-volume coupling suitably incorporating a packing mechanism into a lattice gas with no attractive interactions. On working in a great grand canonical ensemble in which the energy, volume, and number of particles are all allowed to fluctuate simultaneously, the model's mean-field solutions illuminate a strictly first-order transition akin to hard-sphere freezing while describing the thermodynamics of solid and fluid phases. Further implementation of attractive interactions in a natural way allows every aspect of the phase diagram of a simple substance to be reproduced, thereby accomplishing the van der Waals picture of the states of matter from first principles of statistical mechanics. This fairly accurate qualitative description plausibly renders mean-field theory a reasonable approach for freezing in three dimensions. At the same time, our mean-field treatment itself suggests freezing to persist in infinitely many dimensions, as advanced from recent simulations [Charbonneau et al., Eur. Phys. J. E 44, 101 (2021)10.1140/epje/s10189-021-00104-y].

Liquid-Liquid Criticality in TIP4P/2005 and Three-State Models of Water

Molecular dynamics simulations leading to the isothermal compressibility, the isobaric thermal expansivity, and the isobaric heat capacity of TIP4P/2005 water are found to be consistent with the coordinates of its second, liquid-liquid critical point reported recently by Debenedetti et al. [ Science 2020, 369, 289-292]. In accord with the theory of critical phenomena, we encounter that the rise in the magnitude of these response functions as temperature is lowered is especially marked along the critical isochore. Furthermore, response-function ratios provide a test for thermodynamic consistency at the critical point and manifest nonuniversal features sharply distinguishing liquid-liquid from standard gas-liquid criticality. The whole pattern of behavior revealed by simulations is qualitatively the same as the one of a three-state Ising model of water exhibiting a low-temperature liquid-liquid critical point. Exact solutions for the two-state components of such a three-state model are also provided.

Supercritical fluids behave as complex networks

Supercritical fluids play a key role in environmental, geological, and celestial processes, and are of great importance to many scientific and engineering applications. They exhibit strong variations in thermodynamic response functions, which has been hypothesized to stem from the microstructural behavior. However, a direct connection between thermodynamic conditions and the microstructural behavior, as described by molecular clusters, remains an outstanding issue. By utilizing a first-principles-based criterion and self-similarity analysis, we identify energetically localized molecular clusters whose size distribution and connectivity exhibit self-similarity in the extended supercritical phase space. We show that the structural response of these clusters follows a complex network behavior whose dynamics arises from the energetics of isotropic molecular interactions. Furthermore, we demonstrate that a hidden variable network model can accurately describe the structural and dynamical response of supercritical fluids. These results highlight the need for constitutive models and provide a basis to relate the fluid microstructure to thermodynamic response functions.

Density anomaly in water-alcohol mixtures: Minimum model for structure makers and breakers

We modeled the change in the temperature of maximum density (TMD) of a waterlike solvent when small amounts of solute are added to the mixture. The solvent is modeled as a two length scales potential, which is known to exhibit waterlike characteristic anomalies, while the solute is chosen to have an attractive interaction with the solvent which is tuned from small to large attractive potential. We show that if the solute exhibits high attraction with the solvent it behaves as a structure maker and the TMD increases with the addition of solute, while if the solute shows a low attraction with the solvent the TMD decreases, with the solute behaving as a structure breaker.

Correlated Fluctuations of Structural Indicators Close to the Liquid-Liquid Transition in Supercooled Water

Multiple numerical studies have unambiguously shown the existence of a liquid-liquid critical point in supercooled states for different numerical models of water, and various structural indicators have been put forward to describe the transformation associated with this phase transition. Here we analyze numerical simulations of near-critical supercooled water to compare the behavior of several of such indicators with critical density fluctuations. We show that close to the critical point most indicators are strongly correlated to density, and some of them even display identical distributions of fluctuations. These indicators probe the exact same free energy landscape, therefore providing a thermodynamic description of critical supercooled water which is identical to that provided by the density order parameter. This implies that close to the critical point, there is a tight coupling between many, only apparently distinct, structural degrees of freedom.

Water's Unusual Thermodynamics in the Realm of Physical Chemistry

While it is known since the early work by Edsall, Frank and Evans, Kauzmann, and others that the thermodynamics of solvation of nonpolar solutes in water is unusual and has implications for the thermodynamics of protein folding, only recently have its connections with the unusual temperature dependence of the density of solvent water been illuminated. Such density behavior is, in turn, one of the manifestations of a nonstandard thermodynamic pattern contemplating a second, liquid-liquid critical point at conditions of temperature and pressure at which water exists as a deeply supercooled liquid. Recent experimental and computational work unambiguously points toward the existence of such a critical point, thereby providing concrete answers to the questions posed by the 1976 pioneering experiments by Speedy and Angell and the associated "liquid-liquid transition hypothesis" posited in 1992 by Stanley and co-workers. Challenges of this phenomenology to the branch of Statistical Mechanics remain.

Minimal Microscopic Model for Liquid Polyamorphism and Waterlike Anomalies

Liquid polyamorphism is the intriguing possibility for a single component substance to exist in multiple liquid phases. We propose a minimal model for this phenomenon. Starting with a binary lattice model with critical azeotropy and liquid-liquid demixing, we allow interconversion of the two species, turning the system into a single-component fluid with two states differing in energy and entropy. Unveiling the phase diagram of the noninterconverting binary mixture gives unprecedented insight on the phase behaviors accessible to the interconverting fluid, such as a liquid-liquid transition with a critical point, or a singularity-free scenario, exhibiting thermodynamic anomalies without polyamorphism. The model provides a unified theoretical framework to describe supercooled water and a variety of polyamorphic liquids with waterlike anomalies.

Epidemics, the Ising-model and percolation theory: A comprehensive review focused on Covid-19

We revisit well-established concepts of epidemiology, the Ising-model, and percolation theory. Also, we employ a spin S = 1/2 Ising-like model and a (logistic) Fermi-Dirac-like function to describe the spread of Covid-19. Our analysis show that: (i) in many cases the epidemic curve can be described by a Gaussian-type function; (ii) the temporal evolution of the accumulative number of infections and fatalities follow a logistic function; (iii) the key role played by the quarantine to block the spread of Covid-19 in terms of an interacting parameter between people. In the frame of elementary percolation theory, we show that: (i) the percolation probability can be associated with the probability of a person being infected with Covid-19; (ii) the concepts of blocked and non-blocked connections can be associated, respectively, with a person respecting or not the social distancing. Yet, we make a connection between epidemiological concepts and well-established concepts in condensed matter Physics.

Enhanced Grüneisen Parameter in Supercooled Water

We use the recently-proposed compressible cell Ising-like model to estimate the ratio between thermal expansivity and specific heat (the Grüneisen parameter Γs) in supercooled water. Near the critical pressure and temperature, Γs becomes significantly sensitive to thermal fluctuations of the order-parameter, a characteristic behavior of pressure-induced critical points. Such enhancement of Γs indicates that two energy scales are governing the system, namely the coexistence of high- and low-density liquids, which become indistinguishable at the critical point in the supercooled phase. The temperature dependence of the compressibility, sound velocity and pseudo-Grüneisen parameter Γw are also reported. Our findings support the proposed liquid-liquid critical point in supercooled water in the No-Man's Land regime, and indicates possible applications of this model to other systems. In particular, an application of the model to the qualitative behavior of the Ising-like nematic phase in Fe-based superconductors is also presented.