Local functional models of critical correlations in thin-films

Recent work on local functional theories of critical inhomogeneous fluids and Ising-like magnets has shown them to be a potentially exact, or near exact, description of universal finite-size effects associated with the excess free-energy and scaling of one-point functions in critical thin films. This approach is extended to predict the two-point correlation function G in critical thin-films with symmetric surface fields in arbitrary dimension d. In d=2 we show there is exact agreement with the predictions of conformal invariance for the complete spectrum of correlation lengths as well as the detailed position dependence of the asymptotic decay of G. In d=3 and d>=4 we present new numerical predictions for the universal finite-size correlation length and scaling functions determining the structure of G across the thin-film. Highly accurate analytical closed form expressions for these universal properties are derived in arbitrary dimension.Comment: 4 pages, 1 postscript figure. Submitted to Phys Rev Let

Coexistence and Criticality in Size-Asymmetric Hard-Core Electrolytes

Liquid-vapor coexistence curves and critical parameters for hard-core 1:1 electrolyte models with diameter ratios lambda = sigma_{-}/\sigma_{+}=1 to 5.7 have been studied by fine-discretization Monte Carlo methods. Normalizing via the length scale sigma_{+-}=(sigma_{+} + sigma_{-})/2 relevant for the low densities in question, both Tc* (=kB Tc sigma_{+-}/q^2 and rhoc* (= rhoc sigma _{+-}^{3}) decrease rapidly (from ~ 0.05 to 0.03 and 0.08 to 0.04, respectively) as lambda increases. These trends, which unequivocally contradict current theories, are closely mirrored by results for tightly tethered dipolar dimers (with Tc* lower by ~ 0-11% and rhoc* greater by 37-12%).Comment: 4 pages, 5 figure

Anomalous Fluctuations of Directed Polymers in Random Media

A systematic analysis of large scale fluctuations in the low temperature pinned phase of a directed polymer in a random potential is described. These fluctuations come from rare regions with nearly degenerate ``ground states''. The probability distribution of their sizes is found to have a power law tail. The rare regions in the tail dominate much of the physics. The analysis presented here takes advantage of the mapping to the noisy-Burgers' equation. It complements a phenomenological description of glassy phases based on a scaling picture of droplet excitations and a recent variational approach with ``broken replica symmetry''. It is argued that the power law distribution of large thermally active excitations is a consequence of the continuous statistical ``tilt'' symmetry of the directed polymer, the breaking of which gives rise to the large active excitations in a manner analogous to the appearance of Goldstone modes in pure systems with a broken continuous symmetry.Comment: 59 pages including 8 figures ( REVTEX 3.0 )E-mail: [email protected]

Dynamics and transport in random quantum systems governed by strong-randomness fixed points

We present results on the low-frequency dynamical and transport properties of random quantum systems whose low temperature ($T$), low-energy behavior is controlled by strong disorder fixed points. We obtain the momentum and frequency dependent dynamic structure factor in the Random Singlet (RS) phases of both spin-1/2 and spin-1 random antiferromagnetic chains, as well as in the Random Dimer (RD) and Ising Antiferromagnetic (IAF) phases of spin-1/2 random antiferromagnetic chains. We show that the RS phases are unusual `spin metals' with divergent low-frequency spin conductivity at T=0, and we also follow the conductivity through novel `metal-insulator' transitions tuned by the strength of dimerization or Ising anisotropy in the spin-1/2 case, and by the strength of disorder in the spin-1 case. We work out the average spin and energy autocorrelations in the one-dimensional random transverse field Ising model in the vicinity of its quantum critical point. All of the above calculations are valid in the frequency dominated regime \omega \agt T, and rely on previously available renormalization group schemes that describe these systems in terms of the properties of certain strong-disorder fixed point theories. In addition, we obtain some information about the behavior of the dynamic structure factor and dynamical conductivity in the opposite `hydrodynamic' regime $\omega < T$ for the special case of spin-1/2 chains close to the planar limit (the quantum x-y model) by analyzing the corresponding quantities in an equivalent model of spinless fermions with weak repulsive interactions and particle-hole symmetric disorder.Comment: Long version (with many additional results) of Phys. Rev. Lett. {\bf 84}, 3434 (2000) (available as cond-mat/9904290); two-column format, 33 pages and 8 figure

Short-time dynamics in the 1D long-range Potts model

We present numerical investigations of the short-time dynamics at criticality in the 1D Potts model with power-law decaying interactions of the form 1/r^{1+sigma}. The scaling properties of the magnetization, autocorrelation function and time correlations of the magnetization are studied. The dynamical critical exponents theta' and z are derived in the cases q=2 and q=3 for several values of the parameter $\sigma$ belonging to the nontrivial critical regime.Comment: 8 pages, 8 figures, minor changes - several typos fixed, one reference change

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

Optimized energy calculation in lattice systems with long-range interactions

We discuss an efficient approach to the calculation of the internal energy in numerical simulations of spin systems with long-range interactions. Although, since the introduction of the Luijten-Bl\"ote algorithm, Monte Carlo simulations of these systems no longer pose a fundamental problem, the energy calculation is still an O(N^2) problem for systems of size N. We show how this can be reduced to an O(N logN) problem, with a break-even point that is already reached for very small systems. This allows the study of a variety of, until now hardly accessible, physical aspects of these systems. In particular, we combine the optimized energy calculation with histogram interpolation methods to investigate the specific heat of the Ising model and the first-order regime of the three-state Potts model with long-range interactions.Comment: 10 pages, including 8 EPS figures. To appear in Phys. Rev. E. Also available as PDF file at http://www.cond-mat.physik.uni-mainz.de/~luijten/erikpubs.htm

The bulk correlation length and the range of thermodynamic Casimir forces at Bose-Einstein condensation

The relation between the bulk correlation length and the decay length of thermodynamic Casimir forces is investigated microscopically in two three-dimensional systems undergoing Bose-Einstein condensation: the perfect Bose gas and the imperfect mean-field Bose gas. For each of these systems, both lengths diverge upon approaching the corresponding condensation point from the one-phase side, and are proportional to each other. We determine the proportionality factors and discuss their dependence on the boundary conditions. The values of the corresponding critical exponents for the decay length and the correlation length are the same, equal to 1/2 for the perfect gas, and 1 for the imperfect gas

Critical energy-density profile near walls

We examine critical adsorption for semi-infinite thermodynamic systems of the Ising universality class when they are in contact with a wall of the so-called normal surface universality class in spatial dimension d=3 and in the mean-field limit. We apply local-functional theory and Monte Carlo simulations in order to quantitatively determine the properties of the energy density as the primary scaling density characterizing the critical behaviors of Ising systems besides the order parameter. Our results apply to the critical isochore, near two-phase coexistence, and along the critical isotherm if the surface and the weak bulk magnetic fields are either collinear or anticollinear. In the latter case, we also consider the order parameter, which so far has yet to be examined along these lines. We find the interface between the surface and the bulk phases at macroscopic distances from the surface, i.e., the surface is “wet.” It turns out that in this case the usual property of monotonicity of primary scaling densities with respect to the temperature or magnetic field scaling variable does not hold for the energy density due to the presence of this interface

Persistence in Cluster--Cluster Aggregation

Persistence is considered in diffusion--limited cluster--cluster aggregation, in one dimension and when the diffusion coefficient of a cluster depends on its size $s$ as $D(s) \sim s^\gamma$. The empty and filled site persistences are defined as the probabilities, that a site has been either empty or covered by a cluster all the time whereas the cluster persistence gives the probability of a cluster to remain intact. The filled site one is nonuniversal. The empty site and cluster persistences are found to be universal, as supported by analytical arguments and simulations. The empty site case decays algebraically with the exponent $\theta_E = 2/(2 - \gamma)$. The cluster persistence is related to the small $s$ behavior of the cluster size distribution and behaves also algebraically for $0 \le \gamma < 2$ while for $\gamma < 0$ the behavior is stretched exponential. In the scaling limit $t \to \infty$ and $K(t) \to \infty$ with $t/K(t)$ fixed the distribution of intervals of size $k$ between persistent regions scales as $n(k;t) = K^{-2} f(k/K)$, where $K(t) \sim t^\theta$ is the average interval size and $f(y) = e^{-y}$. For finite $t$ the scaling is poor for $k \ll t^z$, due to the insufficient separation of the two length scales: the distances between clusters, $t^z$, and that between persistent regions, $t^\theta$. For the size distribution of persistent regions the time and size dependences separate, the latter being independent of the diffusion exponent $\gamma$ but depending on the initial cluster size distribution.Comment: 14 pages, 12 figures, RevTeX, submitted to Phys. Rev.