Asymptotic Expansions for lambda_d of the Dimer and Monomer-Dimer Problems

In the past few years we have derived asymptotic expansions for lambda_d of the dimer problem and lambda_d(p) of the monomer-dimer problem. The many expansions so far computed are collected herein. We shine a light on results in two dimensions inspired by the work of M. E. Fisher. Much of the work reported here was joint with Shmuel Friedland.Comment: 4 page

Numerical studies of the two- and three-dimensional gauge glass at low temperature

We present results from Monte Carlo simulations of the two- and three-dimensional gauge glass at low temperature using the parallel tempering Monte Carlo method. Our results in two dimensions strongly support the transition being at T_c=0. A finite-size scaling analysis, which works well only for the larger sizes and lower temperatures, gives the stiffness exponent theta = -0.39 +/- 0.03. In three dimensions we find theta = 0.27 +/- 0.01, compatible with recent results from domain wall renormalization group studies.Comment: 7 pages, 10 figures, submitted to PR

Soluble `Supersymmetric' Quantum XY Model

We present a `supersymmetric' modification of the $d$-dimensional quantum rotor model whose ground state is exactly soluble. The model undergoes a vortex-binding transition from insulator to metal as the rotor coupling is varied. The Hamiltonian contains three-site terms which are relevant: they change the universality class of the transition from that of the ($d+1$)--- to the $d$-dimensional classical XY model. The metallic phase has algebraic ODLRO but the superfluid density is identically zero. Variational wave functions for single-particle and collective excitations are presented.Comment: 12 pages, REVTEX 3.0, IUCM93-00

Depinning with dynamic stress overshoots: A hybrid of critical and pseudohysteretic behavior

A model of an elastic manifold driven through a random medium by an applied force F is studied focussing on the effects of inertia and elastic waves, in particular {\it stress overshoots} in which motion of one segment of the manifold causes a temporary stress on its neighboring segments in addition to the static stress. Such stress overshoots decrease the critical force for depinning and make the depinning transition hysteretic. We find that the steady state velocity of the moving phase is nevertheless history independent and the critical behavior as the force is decreased is in the same universality class as in the absence of stress overshoots: the dissipative limit which has been studied analytically. To reach this conclusion, finite-size scaling analyses of a variety of quantities have been supplemented by heuristic arguments. If the force is increased slowly from zero, the spectrum of avalanche sizes that occurs appears to be quite different from the dissipative limit. After stopping from the moving phase, the restarting involves both fractal and bubble-like nucleation. Hysteresis loops can be understood in terms of a depletion layer caused by the stress overshoots, but surprisingly, in the limit of very large samples the hysteresis loops vanish. We argue that, although there can be striking differences over a wide range of length scales, the universality class governing this pseudohysteresis is again that of the dissipative limit. Consequences of this picture for the statistics and dynamics of earthquakes on geological faults are briefly discussed.Comment: 43 pages, 57 figures (yes, that's a five followed by a seven), revte

An Asymptotic Expansion and Recursive Inequalities for the Monomer-Dimer Problem

Let (lambda_d)(p) be the p monomer-dimer entropy on the d-dimensional integer lattice Z^d, where p in [0,1] is the dimer density. We give upper and lower bounds for (lambda_d)(p) in terms of expressions involving (lambda_(d-1))(q). The upper bound is based on a conjecture claiming that the p monomer-dimer entropy of an infinite subset of Z^d is bounded above by (lambda_d)(p). We compute the first three terms in the formal asymptotic expansion of (lambda_d)(p) in powers of 1/d. We prove that the lower asymptotic matching conjecture is satisfied for (lambda_d)(p).Comment: 15 pages, much more about d=1,2,

Nonequilibrium dynamics of random field Ising spin chains: exact results via real space RG

Non-equilibrium dynamics of classical random Ising spin chains are studied using asymptotically exact real space renormalization group. Specifically the random field Ising model with and without an applied field (and the Ising spin glass (SG) in a field), in the universal regime of a large Imry Ma length so that coarsening of domains after a quench occurs over large scales. Two types of domain walls diffuse in opposite Sinai random potentials and mutually annihilate. The domain walls converge rapidly to a set of system-specific time-dependent positions {\it independent of the initial conditions}. We obtain the time dependent energy, magnetization and domain size distribution (statistically independent). The equilibrium limits agree with known exact results. We obtain exact scaling forms for two-point equal time correlation and two-time autocorrelations. We also compute the persistence properties of a single spin, of local magnetization, and of domains. The analogous quantities for the spin glass are obtained. We compute the two-point two-time correlation which can be measured by experiments on spin-glass like systems. Thermal fluctuations are found to be dominated by rare events; all moments of truncated correlations are computed. The response to a small field applied after waiting time $t_w$, as measured in aging experiments, and the fluctuation-dissipation ratio $X(t,t_w)$ are computed. For $(t-t_w) \sim t_w^{\hat{\alpha}}$, $\hat{\alpha} <1$, it equals its equilibrium value X=1, though time translational invariance fails. It exhibits for $t-t_w \sim t_w$ aging regime with non-trivial $X=X(t/t_w) \neq 1$, different from mean field.Comment: 55 pages, 9 figures, revte

Scaling determination of the nonlinear I-V characteristics for 2D superconducting networks

It is shown from computer simulations that the current-voltage ($I$-$V$) characteristics for the two-dimensional XY model with resistively-shunted Josephson junction dynamics and Monte Carlo dynamics obeys a finite-size scaling form from which the nonlinear $I$-$V$ exponent $a$ can be determined to good precision. This determination supports the conclusion $a=z+1$, where $z$ is the dynamic critical exponent. The results are discussed in the light of the contrary conclusion reached by Tang and Chen [Phys. Rev. B {\bf 67}, 024508 (2003)] and the possibility of a breakdown of scaling suggested by Bormann [Phys. Rev. Lett. {\bf 78}, 4324 (1997)].Comment: 6 pages, to appear in PR

Magnetic Field induced Dimensional Crossover Phenomena in Cuprate Superconductors and their Implications

We discuss the occurrence of crossing points in the magnetization - temperature $(m,T$) plane within the framework of critical phenomena. It is shown that in a two-dimensional superconducting slab of thickness $d_{s}$ $m_{z}(\delta)$ versus temperature $T$ curves measured in different fields $\mathbf{H} = H(0,\sin (\delta) ,\cos (\delta))$ will cross at the critical temperature T_c of the slab. In contrast, in a 3D anisotropic bulk superconductor the crossing point occurs in the plot $m_{z}(\delta) /H_{z}^{1/2}$ versus $T$. The experimental facts that 2D crossing point features have been observed in ceramics and in single crystals for $\mathbf{H}$ close to $\mathbf{H} = H(0,0,1)$, but not for $\mathbf{H} = H(0,1,0)$, is explained in terms of an angle-dependent crossover field separating the regions where 2D or 3D thermal fluctuations dominate. The measured 2D-crossing point data are used to estimate one of the fundamental parameters of cuprate superconductors, the minimum thickness of the slab $(d_{s})$, which remains superconducting. Our estimates, based on experimental 2D-crossing point data for single crystals, reveal that this length adopts material dependent values. Therefore, experimental data for T_c and $\lambda_{\Vert}^{2}(T=0)$, plotted in terms of T_c versus $1/\lambda_{\Vert}^{2}(T=0)$ will not tend to a straight line with universal slope as the underdoped limit is approached. Implications for magnetic torque measurements are also worked out

Ring exchange, the Bose metal, and bosonization in two dimensions

Motivated by the high-T_c cuprates, we consider a model of bosonic Cooper pairs moving on a square lattice via ring exchange. We show that this model offers a natural middle ground between a conventional antiferromagnetic Mott insulator and the fully deconfined fractionalized phase which underlies the spin-charge separation scenario for high-T_c superconductivity. We show that such ring models sustain a stable critical phase in two dimensions, the *Bose metal*. The Bose metal is a compressible state, with gapless but uncondensed boson and ``vortex'' excitations, power-law superconducting and charge-ordering correlations, and broad spectral functions. We characterize the Bose metal with the aid of an exact plaquette duality transformation, which motivates a universal low energy description of the Bose metal. This description is in terms of a pair of dual bosonic phase fields, and is a direct analog of the well-known one-dimensional bosonization approach. We verify the validity of the low energy description by numerical simulations of the ring model in its exact dual form. The relevance to the high-T_c superconductors and a variety of extensions to other systems are discussed, including the bosonization of a two dimensional fermionic ring model

Surface and capillary transitions in an associating binary mixture model

We investigate the phase diagram of a two-component associating fluid mixture in the presence of selectively adsorbing substrates. The mixture is characterized by a bulk phase diagram which displays peculiar features such as closed loops of immiscibility. The presence of the substrates may interfere the physical mechanism involved in the appearance of these phase diagrams, leading to an enhanced tendency to phase separate below the lower critical solution point. Three different cases are considered: a planar solid surface in contact with a bulk fluid, while the other two represent two models of porous systems, namely a slit and an array on infinitely long parallel cylinders. We confirm that surface transitions, as well as capillary transitions for a large area/volume ratio, are stabilized in the one-phase region. Applicability of our results to experiments reported in the literature is discussed.Comment: 12 two-column pages, 12 figures, accepted for publication in Physical Review E; corrected versio