Critical Casimir forces along the iso-fields

Using quasi-exact numerical density-matrix renormalization-group techniques we calculate the critical Casimir force for a two-dimensional (2D) Ising strip with equal strong surface fields, along the thermodynamic paths corresponding to the fixed nonzero bulk field h0. Using the Derjaguin approximation we also determine the critical Casimir force and its potential for two discs. We find that varying the temperature along the iso-fields lying between the bulk coexistence and the capillary condensation critical point leads to a dramatic increase of the critical Casimir interactions with a qualitatively different functional dependence on the temperature than along h=0. These findings might be of relevance for biomembranes, whose heterogeneity is recently interpreted as being connected with a critical behavior belonging to the 2D Ising universality class.Comment: 9 pages, 12 figures, submitted to Physical Review

Solvation force for long ranged wall-fluid potentials

The solvation force of a simple fluid confined between identical planar walls is studied in two model systems with short ranged fluid-fluid interactions and long ranged wall-fluid potentials decaying as $-Az^{-p}, z\to \infty$, for various values of $p$. Results for the Ising spins system are obtained in two dimensions at vanishing bulk magnetic field $h=0$ by means of the density-matrix renormalization-group method; results for the truncated Lennard-Jones (LJ) fluid are obtained within the nonlocal density functional theory. At low temperatures the solvation force $f_{solv}$ for the Ising film is repulsive and decays for large wall separations $L$ in the same fashion as the boundary field $f_{solv}\sim L^{-p}$, whereas for temperatures larger than the bulk critical temperature $f_{solv}$ is attractive and the asymptotic decay is $f_{solv}\sim L^{-(p+1)}$. For the LJ fluid system $f_{solv}$ is always repulsive away from the critical region and decays for large $L$ with the the same power law as the wall-fluid potential. We discuss the influence of the critical Casimir effect and of capillary condensation on the behaviour of the solvation force.Comment: 48 pages, 12 figure

Solvation forces in Ising films with long-range boundary fields: density-matrix renormalization-group study

Using the quasi-exact density-matrix renormalization-group method we calculate the solvation forces in two-dimensional Ising films of thickness L subject to identical algebraically decaying boundary fields with various decay exponents p. At the bulk critical point the solvation force acquires a universal contribution which is long-ranged in L due to the critical fluctuations, a phenomenon known as the critical Casimir effect. For p = 2, 3 and 50, we study the scaling behaviour of the solvation force along the pseudo-phase coexistence and along the critical and sub-critical isotherms.Comment: 9 pages, 6 figures, accepted to Molecular Physic

Crossover from Reptation to Rouse dynamics in the Cage Model

The two-dimensional cage model for polymer motion is discussed with an emphasis on the effect of sideways motions, which cross the barriers imposed by the lattice. Using the Density Matrix Method as a solver of the Master Equation, the renewal time and the diffusion coefficient are calculated as a function of the strength of the barrier crossings. A strong crossover influence of the barrier crossings is found and it is analyzed in terms of effective exponents for a given chain length. The crossover scaling functions and the crossover scaling exponents are calculated.Comment: RevTeX, 11 PostScript figures include

On the surface critical behaviour in Ising strips: density-matrix renormalization-group study

Using the density-matrix renormalization-group method we study the surface critical behaviour of the magnetization in Ising strips in the subcritical region. Our results support the prediction that the surface magnetization in the two phases along the pseudo-coexistence curve also behaves as for the ordinary transition below the wetting temperature for the finite value of the surface field.Comment: 15 pages, 9 figure

Influence of Capillary Condensation on the Near-Critical Solvation Force

We argue that in a fluid, or magnet, confined by adsorbing walls which favour liquid, or (+) phase, the solvation (Casimir) force in the vicinity of the critical point is strongly influenced by capillary condensation which occurs below the bulk critical temperature T_c. At T slightly below and above T_c, a small bulk field h<0, which favours gas, or (-) phase, leads to residual condensation and a solvation force which is much more attractive (at the same large wall separation) than that found exactly at the critical point. Our predictions are supported by results obtained from density-matrix renormalization-group calculations in a two-dimensional Ising strip subject to identical surface fields.Comment: 4 Pages, RevTeX, and 3 figures include