The Rubinstein-Duke model for polymer reptation is analyzed by means of density matrix renormalization techniques. It is found that the crossover in the scaling behavior of polymer renewal time (or viscosity) arises from the competing effect of the contribution due to tube length fluctuations and higher-order corrections, which are of opposite sign. Experiments which ought to emphasize both contributions are suggested. The exponent describing the subleading scaling behavior of the diffusion coefficient is also investigated.

Two-dimensional (2D) magnetic materials have attracted much attention due to their unique magnetic properties and promising applications in spintronics. Here, we report on the growth of ferrous chloride (FeCl2) films on Au(111) and graphite with atomic thickness by molecular-beam epitaxy (MBE) and the layer-dependent magnetic properties by density functional theory (DFT) calculations. The growth follows a layer-by-layer mode with adjustable thickness from sub-monolayer to a few layers. Four types of moiré superstructures of a single-layer FeCl2 on graphite and two types of atomic vacancies on Au(111) have been identified based on high-resolution scanning tunneling microscopy (STM). It turned out that the single- and few-layer FeCl2 films grown on Au(111) exhibit a 1T structure. The DFT calculations reveal that a single-layer 1T-FeCl2 has a ferromagnetic ground state. The minimum-energy configuration of a bilayer FeCl2 is satisfied for the 1T–1T structure with ferromagnetic layers coupled antiferromagnetically. These results make FeCl2 a promising candidate as ideal electrodes for spintronic devices providing large magnetoresistance.

We investigate two dimensional critical Ising films of width L with surface fields H(1)=H(L) in the crossover between ordinary (H(1)=0) and normal (H(1)=infinity) transitions. Using exact transfer-matrix diagonalization and density matrix renormalization-group (DMRG) methods, we calculate magnetization profiles m(z), the excess magnetization Gamma, and the analog of the solvation force f(solv) as functions of H1 for several L. Scaling functions of the above quantities deviate substantially from their asymptotic forms at fixed points for a broad region of the scaling variable LH21 approximately L/l(1), where l(1) is the length induced by the surface field H1. The scaling function for /f(solv)/ has a deep minimum near LH(2)(1)=1, which is about one order of magnitude smaller than its value at both fixed points (the "Casimir" amplitude). For weak H1 (l(1)>L) the magnetization profile has a maximum at the center of the film, and f(solv) decays much faster than L-2. For stronger H1 (1>l(1) the solvation force decays according to the universal power law f(solv) approximately L(-2). The results of the approximate DMRG method show remarkable agreement with the exact ones.

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--> infinity, 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) approximately L(-p), whereas for temperatures larger than the bulk critical temperature f(solv) is attractive and the asymptotic decay is f(solv) approximately 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 behavior of the solvation force.

The phase boundaries for corner wetting (filling) in square and diagonal lattice Ising models are exactly determined and show a universal shift relative to wetting near the bulk criticality. More generally, scaling theory predicts that the filling phase boundary shift for wedges and cones is determined by a universal scaling function R(d)(psi) depending only on the opening angle 2psi. R(d)(psi) is determined exactly in d = 2 and approximately in higher dimensions using nonclassical local functional and mean-field theory. Detailed numerical transfer matrix studies of the magnetization profile in finite-size Ising squares support the conjectured connection between filling and the strong-fluctuation regime of wetting.

The effect of gravity on a two dimensional fluid, or Ising magnet, confined between opposing walls is analyzed by density matrix renormalization. Gravity restores two phase coexistence up to the bulk critical point, in agreement with mean field calculations. A detailed finite size scaling analysis of the critical point shift is performed. Density matrix renormalization results are very accurate and the technique is promising and best suited to study equilibrium properties of two dimensional classical systems in contact with walls or with free surfaces.The thermodynamical properties of confined systems have received a lot of attention in the past years [1][2][3][4][5][6][7][8][9][10]. Their critical behavior is rather different from the bulk criticality and has been the subject of extended investigations by means of mean field and scaling analysis [1][2][3][4], Monte Carlo simulations [5-8] and exact calculations [9,10]. The simplest and most studied case is the Ising model in a L × M d−1 lattice with M → ∞, i.e. confined between two infinite walls separated by a finite distance L. Of considerable interest is the situation in which magnetic fields (h 1 and h 2 ) acting on the spins at the walls are introduced.For parallel surface fields (h 1 · h 2 > 0) and finite L two phase coexistence is shifted to finite values of a bulk magnetic field h [1], as illustrated in Fig. 1(a). This phenomenon is analogous to the capillary condensation for a fluid confined between two parallel surfaces, where the gas-liquid transition occurs at a lower pressure than in the bulk. Finite size scaling [1] predicts that the capillary critical point [h c (L), T c (L)] scales as:where T c is the bulk critical temperature and y T = 1/ν, y H = d − β/ν are the thermal and magnetic exponents, respectively (here d is the dimensionality, ν and β are the correlation length and magnetization exponents, respectively). At fixed T < T c and finite L the scaling to the first order line is of type [1]:While the previous relation has been verified in Monte Carlo simulations in d = 2, 3 [6,7], a direct verification of the scaling of the capillary critical point has not been attempted yet, due to the high computational effort [7] needed to locate accurately [h c (L), T c (L)]. The case of opposing surface fields (for simplicity we consider h 1 = −h 2 ) was analyzed in detail by Parry and Evans [2] using a Ginzburg-Landau approach. They found that two phase coexistence is restricted to temperatures below the interface delocalization temperature T d (L) as shown in Fig. 1(a); the surprising result [2] is that T d (L) does not scale to the bulk point T c , for L → ∞, but to the wetting temperature T w as:Here β s is the exponent describing the divergence of the thickness of the wetting layer for a semi infinite system: l ∼ (T w − T ) −βs . We recall also that T w depends on the value of the surface field h 1 and can be far away from the bulk critical point (see Fig. 1(b)). For T d (L) ≤ T < T c there is a single phase [2], with an interface meandering freely ...

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 Tc. At T slightly below and above Tc, 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.PACS numbers: 05.70. Jk, 64.60.Fr, 68.15.+e, 68.35.Rh Finite-size contributions to the free energy of a fluid confined between two parallel walls, separated by a distance L, give rise to a force per unit area between the walls or an excess pressure which is termed the solvation force f solv (L) [1]. This force is, essentially, that which is measured in the surface force apparatus [2]. Theory predicts that at the critical point of a fluid the solvation force becomes long ranged as a result of critical fluctuations [3], a phenomenon which is a direct analog of the well-known Casimir effect in electromagnetism [4]. The existence of the long-ranged critical Casimir force should be common to all systems characterized by fluctuating quantities with external constraints [5]. As yet there has been no direct, unambiguous experimental verification of the critical Casimir effect in fluids [5], although recent experiments do provide indirect evidence for its existence [6]. One of the difficulties is that the predicted leading power law decay of the Casimir force at bulk crit, of the same form as the solvation force arising from dispersion forces. Moreover the amplitude in many systems may be much smaller than the corresponding Hamaker constant [5,7]. The Casimir amplitude A 12 is a universal number, however, its value depends on the type of boundary conditions imposed on the two walls [5]. The most relevant for experiments on pure fluids or for binary mixtures are symmetry breaking boundary conditions, i.e., when the confining walls exert surface fields on molecules in the fluid. Here we exploit the mapping between fluids and the Ising model and consider Ising spin systems subject to identical surface fields h 1 = h 2 > 0. For these systems f solv (L) is expected to be attractive for all thermodynamic states. In d = 2, the Casimir amplitude is known exactly A 11 ≡ A ++ = −π/48 [8], whereas in d = 3 the most recent theoretical result is -0.428 [9] and the Monte Carlo estimate is -0.35 [10]. In this Letter we show that other, near-critical, thermodynamic states exhibit a significantly stronger solvation force (for fixed, large L) than that found exactly at the bulk critical point, and we suggest that this has repercussions for experimental studies.For Ising-like systems with h 1 = h 2 > 0 in vanishing bulk field h = 0, f solv as a fu...

The kinetic Monte Carlo method is used to model the dynamic properties of proton diffusion in anhydrous proton conductors. The results have been discussed with reference to a two-step process called the Grotthuss mechanism. There is a widespread belief that this mechanism is responsible for fast proton mobility. We showed in detail that the relative frequency of reorientation and diffusion processes is crucial for the conductivity. Moreover, the current dependence on proton concentration has been analyzed. In order to test our microscopic model the proton transport in polymer electrolyte membranes based on benzimidazole C(7)H(6)N(2) molecules is studied.