Percolation and cluster Monte Carlo dynamics for spin models

Cluster percolation in the two-dimensional Ising spin glass

Suitable cluster definitions have allowed researchers to describe many ordering transitions in spin systems as geometric phenomena related to percolation. For spin glasses and some other systems with quenched disorder, however, such a connection has not been fully established, and the numerical evidence remains incomplete. Here we use Monte Carlo simulations to study the percolation properties of several classes of clusters occurring in the Edwards-Anderson Ising spin-glass model in two dimensions. The Fortuin-Kasteleyn-Coniglio-Klein clusters originally defined for the ferromagnetic problem do percolate at a temperature that remains nonzero in the thermodynamic limit. On the Nishimori line, this location is accurately predicted by an argument due to Yamaguchi. More relevant for the spin-glass transition are clusters defined on the basis of the overlap of several replicas. We show that various such cluster types have percolation thresholds that shift to lower temperatures by increasing the system size, in agreement with the zero-temperature spin-glass transition in two dimensions. The overlap is linked to the difference in density of the two largest clusters, thus supporting a picture where the spin-glass transition corresponds to an emergent density difference of the two largest clusters inside the percolating phase.

Solution of disordered microphases in the Bethe approximation

The periodic microphases that self-assemble in systems with competing short-range attractive and long-range repulsive (SALR) interactions are structurally both rich and elegant. Significant theoretical and computational efforts have thus been dedicated to untangling their properties. By contrast, disordered microphases, which are structurally just as rich but nowhere near as elegant, have not been as carefully considered. Part of the difficulty is that simple mean-field descriptions make a homogeneity assumption that washes away all of their structural features. Here, we study disordered microphases by exactly solving a SALR model on the Bethe lattice. By sidestepping the homogenization assumption, this treatment recapitulates many of the key structural regimes of disordered microphases, including particle and void cluster fluids as well as gelation. This analysis also provides physical insight into the relationship between various structural and thermal observables, between criticality and physical percolation, and between glassiness and microphase ordering.

Hydrophobic nanoconfinement suppresses fluctuations in supercooled water

We perform very efficient Monte Carlo simulations to study the phase diagram of a water monolayer confined in a fixed disordered matrix of hydrophobic nanoparticles between two hydrophobic plates. We consider different hydrophobic nanoparticle concentrations c. We adopt a coarse-grained model of water that, for c = 0, displays a first-order liquid-liquid phase transition (LLPT) line with negative slope in the pressure-temperature (P-T) plane, ending in a liquid-liquid critical point at about 174 K and 0.13 GPa. We show that upon increase of c the liquid-gas spinodal and the temperature of the maximum density line are shifted with respect to the c = 0 case. We also find dramatic changes in the region around the LLPT. In particular, we observe a substantial (more than 90%) decrease of isothermal compressibility, thermal expansion coefficient and constant-pressure specific heat upon increasing c, consistent with recent experiments. Moreover, we find that a hydrophobic nanoparticle concentration as small as c = 2.4% is enough to destroy the LLPT for P ≥ 0.16 GPa. The fluctuations of volume apparently diverge at P ≈ 0.16 GPa, suggesting that the LLPT line ends in an LL critical point at 0.16 GPa. Therefore, nanoconfinement reduces the range of P-T where the LLPT is observable. By increasing the hydrophobic nanoparticle concentration c, the LLPT becomes weaker and its P-T range smaller. The model allows us to explain these phenomena in terms of a proliferation of interfaces among domains with different local order, promoted by the hydrophobic effect of the water-hydrophobic-nanoparticle interfaces.

Understanding the role of hydrogen bonds in water dynamics and protein stability

The mechanisms of cold and pressure denaturation of proteins are a matter of debate, but it is commonly accepted that water plays a fundamental role in the process. It has been proposed that the denaturation process is related to an increase of hydrogen bonds among hydration water molecules. Other theories suggest that the causes of denaturation are the density fluctuations of surface water, or the destabilization of hydrophobic contacts as a consequence of water molecule inclusions inside the protein, especially at high pressures. We review some theories that have been proposed to give insight into this problem, and we describe a coarse-grained model of water that compares well with experiments for proteins' hydration water. We introduce its extension for a homopolymer in contact with the water monolayer and study it by Monte Carlo simulations in an attempt to understand how the interplay of water cooperativity and interfacial hydrogen bonds affects protein stability.

Effect of hydrophobic environments on the hypothesized liquid-liquid critical point of water

The complex behavior of liquid water, along with its anomalies and their crucial role in the existence of life, continue to attract the attention of researchers. The anomalous behavior of water is more pronounced at subfreezing temperatures and numerous theoretical and experimental studies are directed towards developing a coherent thermodynamic and dynamic framework for understanding supercooled water. The existence of a liquid-liquid critical point in the deep supercooled region has been related to the anomalous behavior of water. However, the experimental study of supercooled water at very low temperatures is hampered by the homogeneous nucleation of the crystal. Recently, water confined in nanoscopic structures or in solutions has attracted interest because nucleation can be delayed. These systems have a tremendous relevance also for current biological advances; e.g., supercooled water is often confined in cell membranes and acts as a solvent for biological molecules. In particular, considerable attention has been recently devoted to understanding hydrophobic interactions or the behavior of water in the presence of apolar interfaces due to their fundamental role in self-assembly of micelles, membrane formation and protein folding. This article reviews and compares two very recent computational works aimed at elucidating the changes in the thermodynamic behavior in the supercooled region and the liquid-liquid critical point phenomenon for water in contact with hydrophobic environments. The results are also compared to previous reports for water in hydrophobic environments.

Understanding diffusion and density anomaly in a coarse-grained model for water confined between hydrophobic walls

We study, by Monte Carlo simulations, a coarse-grained model of a water monolayer between hydrophobic walls at partial hydration, with a wall-to-wall distance of about 0.5 nm. We analyze how the diffusion constant parallel to the walls, D(∥), changes and correlates to the phase diagram of the system. We find a locus of D(∥) maxima and a locus of D(∥) minima along isotherms, with lines of constant D(∥) resembling the melting line of bulk water. The two loci of D(∥) extrema envelope the line of temperatures of density maxima at constant P. We show how these loci are related to the anomalous volume behavior due to the hydrogen bonds. At much lower T, confined water becomes subdiffusive, and we discuss how this behavior is a consequence of the increased correlations among water molecules when the hydrogen bond network develops. Within the subdiffusive region, although translations are largely hampered, we observe that the hydrogen bond network can equilibrate, and its rearrangement is responsible for the appearance of density minima along isobars. We clarify that the minima are not necessarily related to the saturation of the hydrogen bond network.