Cluster analysis for percolation on a two-dimensional fully frustrated system

Fractional Brownian motion of worms in worm algorithms for frustrated Ising magnets

We study the distribution of lengths and other statistical properties of worms constructed by Monte Carlo worm algorithms in the power-law three-sublattice ordered phase of frustrated triangular and kagome lattice Ising antiferromagnets. Viewing each step of the worm construction as a position increment (step) of a random walker, we demonstrate that the persistence exponent θ and the dynamical exponent z of this random walk depend only on the universal power-law exponents of the underlying critical phase and not on the details of the worm algorithm or the microscopic Hamiltonian. Further, we argue that the detailed balance condition obeyed by such worm algorithms and the power-law correlations of the underlying equilibrium system together give rise to two related properties of this random walk: First, the steps of the walk are expected to be power-law correlated in time. Second, the position distribution of the walker relative to its starting point is given by the equilibrium position distribution of a particle in an attractive logarithmic central potential of strength η_{m}, where η_{m} is the universal power-law exponent of the equilibrium defect-antidefect correlation function of the underlying spin system. We derive a scaling relation, z=(2-η_{m})/(1-θ), that allows us to express the dynamical exponent z(η_{m}) of this process in terms of its persistence exponent θ(η_{m}). Our measurements of z(η_{m}) and θ(η_{m}) are consistent with this relation over a range of values of the universal equilibrium exponent η_{m} and yield subdiffusive (z>2) values of z in the entire range. Thus, we demonstrate that the worms represent a discrete-time realization of a fractional Brownian motion characterized by these properties.

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.

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.