Finite Size Effects in Vortex Localization

The equilibrium properties of flux lines pinned by columnar disorder are studied, using the analogy with the time evolution of a diffusing scalar density in a randomly amplifying medium. Near H_{c1}, the physical features of the vortices in the localized phase are shown to be determined by the density of states near the band edge. As a result, H_{c1} is inversely proportional to the logarithm of the sample size, and the screening length of the perpendicular magnetic field decreases with temperature. For large tilt the extended ground state turns out to wander in the plane perpendicular to the defects with exponents corresponding to a directed polymer in a random medium, and the energy difference between two competing metastable states in this case is extensive. The divergence of the effective potential associated with strong pinning centers as the tilt approaches its critical value is discussed as well.Comment: 10 pages, 2 figure

On the magnetization of two-dimensional superconductors

We calculate the magnetization of a two-dimensional superconductor in a perpendicular magnetic field near its Kosterlitz-Thouless transition and at lower temperatures. We find that the critical behavior is more complex than assumed in the literature and that, in particular, the critical magnetization is {\it not} field independent as naive scaling predicts. In the low temperature phase we find a substantial fluctuation renormalization of the mean-field result. We compare our analysis with the data on the cuprates.Comment: 8 pages, 3 figure

Zero Temperature Dynamics of the Weakly Disordered Ising Model

The Glauber dynamics of the pure and weakly disordered random-bond 2d Ising model is studied at zero-temperature. A single characteristic length scale, $L(t)$, is extracted from the equal time correlation function. In the pure case, the persistence probability decreases algebraically with the coarsening length scale. In the disordered case, three distinct regimes are identified: a short time regime where the behaviour is pure-like; an intermediate regime where the persistence probability decays non-algebraically with time; and a long time regime where the domains freeze and there is a cessation of growth. In the intermediate regime, we find that $P(t)\sim L(t)^{-\theta'}$, where $\theta' = 0.420\pm 0.009$. The value of $\theta'$ is consistent with that found for the pure 2d Ising model at zero-temperature. Our results in the intermediate regime are consistent with a logarithmic decay of the persistence probability with time, $P(t)\sim (\ln t)^{-\theta_d}$, where $\theta_d = 0.63\pm 0.01$.Comment: references updated, very minor amendment to abstract and the labelling of figures. To be published in Phys Rev E (Rapid Communications), 1 March 199

Absence of long-range order in a spin-half Heisenberg antiferromagnet on the stacked kagome lattice

We study the ground state of a spin-half Heisenberg antiferromagnet on the stacked kagome lattice by using a spin-rotation-invariant Green's-function method. Since the pure two-dimensional kagome antiferromagnet is most likely a magnetically disordered quantum spin liquid, we investigate the question whether the coupling of kagome layers in a stacked three-dimensional system may lead to a magnetically ordered ground state. We present spin-spin correlation functions and correlation lengths. For comparison we apply also linear spin wave theory. Our results provide strong evidence that the system remains short-range ordered independent of the sign and the strength of the interlayer coupling

Nernst effect in the vortex-liquid regime of a type-II superconductor

We measure the transverse thermoelectric coefficient $\alpha_{xy}$ in simulations of type-II superconductors in the vortex liquid regime, using the time-dependent Ginzburg-Landau (TDGL) equation with thermal noise. Our results are in reasonably good quantitative agreement with experimental data on cuprate samples, suggesting that this simple model of superconducting fluctuations contains much of the physics behind the large Nernst effect observed in these materials.Comment: 6 pages. Expanded version of text. New Fig.

Nonmagnetic Insulating States near the Mott Transitions on Lattices with Geometrical Frustration and Implications for κ\kappa-(ET)2_2Cu2(CN)3_2(CN)_3

We study phase diagrams of the Hubbard model on anisotropic triangular lattices, which also represents a model for $\kappa$-type BEDT-TTF compounds. In contrast with mean-field predictions, path-integral renormalization group calculations show a universal presence of nonmagnetic insulator sandwitched by antiferromagnetic insulator and paramagnetic metals. The nonmagnetic phase does not show a simple translational symmetry breakings such as flux phases, implying a genuine Mott insulator. We discuss possible relevance on the nonmagnetic insulating phase found in $\kappa$-(ET)$_2$Cu$_2(CN)_3$.Comment: 4pages including 7 figure

Marginal Pinning of Quenched Random Polymers

An elastic string embedded in 3D space and subject to a short-range correlated random potential exhibits marginal pinning at high temperatures, with the pinning length $L_c(T)$ becoming exponentially sensitive to temperature. Using a functional renormalization group (FRG) approach we find $L_c(T) \propto \exp[(32/\pi)(T/T_{\rm dp})^3]$, with $T_{\rm dp}$ the depinning temperature. A slow decay of disorder correlations as it appears in the problem of flux line pinning in superconductors modifies this result, $\ln L_c(T)\propto T^{3/2}$.Comment: 4 pages, RevTeX, 1 figure inserte

Simulation Studies on the Stability of the Vortex-Glass Order

The stability of the three-dimensional vortex-glass order in random type-II superconductors with point disorder is investigated by equilibrium Monte Carlo simulations based on a lattice XY model with a uniform field threading the system. It is found that the vortex-glass order, which stably exists in the absence of screening, is destroyed by the screenng effect, corroborating the previous finding based on the spatially isotropic gauge-glass model. Estimated critical exponents, however, deviate considerably from the values reported for the gauge-glass model.Comment: Minor modifications made, a few referenced added; to appear in J. Phys. Soc. Jpn. Vol.69 No.1 (2000

U(1) spin liquids and valence bond solids in a large-N three-dimensional Heisenberg model

We study possible quantum ground states of the Sp(N) generalized Heisenberg model on a cubic lattice with nearest-neighbor and next-nearest-neighbor exchange interactions. The phase diagram is obtained in the large-N limit and fluctuation effects are considered via appropriate gauge theories. In particular, we find three U(1) spin liquid phases with different short-range magnetic correlations. These phases are characterized by deconfined gapped spinons, gapped monopoles, and gapless ``photons''. As N becomes smaller, a confinement transition from these phases to valence bond solids (VBS) may occur. This transition is studied by using duality and analyzing the resulting theory of monopoles coupled to a non-compact dual gauge field; the condensation of the monopoles leads to VBS phases. We determine the resulting VBS phases emerging from two of the three spin liquid states. On the other hand, the spin liquid state near J_1 \approx J_2 appears to be more stable against monopole condensation and could be a promising candidate for a spin liquid state in real systems.Comment: revtex file 12 pages, 17 figure

Fragility of the Free-Energy Landscape of a Directed Polymer in Random Media

We examine the sensitiveness of the free-energy landscape of a directed polymer in random media with respect to various kinds of infinitesimally weak perturbation including the intriguing case of temperature-chaos. To this end, we combine the replica Bethe ansatz approach outlined in cond-mat/0112384, the mapping to a modified Sinai model and numerically exact calculations by the transfer-matrix method. Our results imply that for all the perturbations under study there is a slow crossover from a weakly perturbed regime where rare events take place to a strongly perturbed regime at larger length scales beyond the so called overlap length where typical events take place leading to chaos, i.e. a complete reshuffling of the free-energy landscape. Within the replica space, the evidence for chaos is found in the factorization of the replicated partition function induced by infinitesimal perturbations. This is the reflex of explicit replica symmetry breaking.Comment: 29 pages, Revtex4, ps figure