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At least 1,135 records · Page 63Linked to original sources
arXiv2000

Boolean derivatives and computation of cellular automata

The derivatives of a Boolean function are defined up to any order. The Taylor and MacLaurin expansions of a Boolean function are thus obtained. The last corresponds to the ring sum expansion (RSE) of a Boolean function, and is a more compact form than the usual canonical disjunctive form. For totalistic functions the RSE allows the saving of a large number of Boolean operations. The algorithm has natural applications to the simulations of cellular automata using the multi site coding technique. Several already published algorithms are analized, and expressions with fewer terms are generally found.

cond-mat↗
arXiv1992

Fluctuating Interfaces, Surface Tension, and Capillary Waves: An Introduction

We present an introduction to modern theories of interfacial fluctuations and the associated interfacial parameters: surface tension and surface stiffness, as well as their interpretation within the capillary wave model. Transfer matrix spectrum properties due to fluctuation of an interface in a long-cylinder geometry are reviewed. The roughening transition and properties of rigid interfaces below the roughening temperature in 3d lattice models are surveyed with emphasis on differences in fluctuations and transfer matrix spectral properties of rigid vs. rough interfaces.

cond-mat↗
arXiv1994

Localization in Lattice Gauge Theory and a New Multigrid Method

We show numerically that the lowest eigenmodes of the 2-dimensional Laplace-operator with SU(2) gauge couplings are strongly localized. A connection is drawn to the Anderson-Localization problem. A new Multigrid algorithm, capable to deal with these modes, shows no critical slowing down for this problem.

hep-lat↗
arXiv1996

Power Laws are Logarithmic Boltzmann Laws

Multiplicative random processes in (not necessaryly equilibrium or steady state) stochastic systems with many degrees of freedom lead to Boltzmann distributions when the dynamics is expressed in terms of the logarithm of the normalized elementary variables. In terms of the original variables this gives a power-law distribution. This mechanism implies certain relations between the constraints of the system, the power of the distribution and the dispersion law of the fluctuations. These predictions are validated by Monte Carlo simulations and experimental data. We speculate that stochastic multiplicative dynamics might be the natural origin for the emergence of criticality and scale hierarchies without fine-tuning.

adap-org↗
arXiv1994

The Higgs model for anyons and Liouville action: Chaotic spectrum, energy gap and exclusion principle

Geodesic completness and self-adjointness imply that the Hamiltonian for anyons is the Laplacian with respect to the Weil-Petersson metric. This metric is complete on the Deligne-Mumford compactification of moduli (configuration) space. The structure of this compactification fixes the possible anyon configurations. This allows us to identify anyons with singularities (elliptic points with ramification $q^{-1}$) in the Poincaré metric implying that anyon spectrum is chaotic for $n\ge 3$. Furthermore, the bound on the holomorphic sectional curvature of moduli spaces implies a gap in the energy spectrum. For $q=0$ (punctures) anyons are infinitely separated in the Poincaré metric (hard-core). This indicates that the exclusion principle has a geometrical intepretation. Finally we give the differential equation satisfied by the generating function for volumes of the configuration space of anyons.

hep-th↗
arXiv1995

Type II Anyon Superconductivity

Assuming that the superconductivity which is described by the low energy effective action of the anyon system may be type II, we discuss its characteristics. We also study physical properties of the Chern-Simons vortices, which may be formed as the external magnetic field is applied to the system, such as their statistics, the free energy of single vortex and the interaction energy between two vortices.

cond-mat↗
arXiv1996

Fusion & Tensoring of Conformal Field Theory and Composite Fermion Picture of Fractional Quantum Hall Effect

We propose a new way for describing the transition between two quantum Hall effect states with different filling factors within the framework of rational conformal field theory. Using a particular class of non-unitary theories, we explicitly recover Jain's picture of attaching flux quanta by the fusion rules of primary fields. Filling higher Landau levels of composite fermions can be described by taking tensor products of conformal theories. The usual projection to the lowest Landau level corresponds then to a simple coset of these tensor products with several U(1)-theories divided out. These two operations -- the fusion map and the tensor map -- can explain the Jain series and all other observed fractions as exceptional cases. Within our scheme of transitions we naturally find a field with the experimentally observed universal critical exponent 7/3.

hep-th↗
arXiv1994

Critical Temperature and Amplitude Ratios from a Finite-Temperature Renormalization Group

We study $ł\f^4$ theory using an environmentally friendly finite-temperature renormalization group. We derive flow equations, using a fiducial temperature as flow parameter, develop them perturbatively in an expansion free from ultraviolet and infrared divergences, then integrate them numerically from zero to temperatures above the critical temperature. The critical temperature, at which the mass vanishes, is obtained by integrating the flow equations and is determined as a function of the zero-temperature mass and coupling. We calculate the field expectation value and minimum of the effective potential as functions of temperature and derive some universal amplitude ratios which connect the broken and symmetric phases of the theory. The latter are found to be in good agreement with those of the three-dimensional Ising model obtained from high- and low-temperature series expansions.

hep-th↗
arXiv1995

Mean Field Description of the Fractional Quantum Hall Effect Near $ν=1/(2k+1)$

The nature of Mean Field Solutions to the Equations of Motion of the Chern--Simons Landau--Ginsberg (CSLG) description of the Fractional Quantum Hall Effect (FQHE) is studied. Beginning with the conventional description of this model at some chemical potential $μ_0$ and magnetic field $B$ corresponding to a ``special'' filling fraction $ν=2πρ/eB=1/n$ ($n=1,3,5\cdot \cdot\cdot$) we show that a deviation of $μ$ in a finite range around $μ_0$ does not change the Mean Field solution and thus the mean density of particles in the model. This result holds not only for the lowest energy Mean Field solution but for the vortex excitations as well. The vortex configurations do not depend on $μ$ in a finite range about $μ_0$ in this model. However when $μ-μ_0 < μ_{cr}^-$ (or $μ-μ_0>μ_{cr}^+$) the lowest energy Mean Field solution describes a condensate of vortices (or antivortices). We give numerical examples of vortex and antivortex configurations and discuss the range of $μ$ and $ν$ over which the system of vortices is dilute.

hep-th↗
arXiv1995

PHASE TRANSITION OF N-COMPONENT SUPERCONDUCTORS

We investigate the phase transition in the three-dimensional abelian Higgs model for N complex scalar fields, using the gauge-invariant average action Γ_{k}. The dependence of Γ_{k} on the effective infra-red cut-off k is described by a non-perturbative flow equation. The transition turns out to be first- or second-order, depending on the ratio between scalar and gauge coupling. We look at the fixed points of the theory for various N and compute the critical exponents of the model. Comparison with results from the ε-expansion shows a rather poor convergence for ε=1 even for large N. This is in contrast to the surprisingly good results of the ε-expansion for pure scalar theories. Our results suggest the existence of a parameter range with a second-order transition for all N, including the case of the superconductor phase transition for N=1.

cond-mat↗
arXiv1992

Hierarchical Wave Functions and Fractional Statistics in Fractional Quantum Hall Effect on the Torus

One kind of hierarchical wave functions of Fractional Quantum Hall Effect (FQHE) on the torus are constructed. The multi-component nature of anyon wave functions and the degeneracy of FQHE on the torus are very clear reflected in this kind of wave functions. We also calculate the braid statistics of the quasiparticles in FQHE on the torus and show they fit to the picture of anyons interacting with magnetic field on the torus obtained from braid group analysis.

cond-mat↗
arXiv1994

Mutifractal Analysis of Broadly Distributed Observables at Criticality

The multifractal analysis of disorder induced localization-delocalization transitions is reviewed. Scaling properties of this transition are generic for multi parameter coherent systems which show broadly distributed observables at criticality. The multifractal analysis of local measures is extended to more general observables including scaling variables such as the conductance in the localization problem. The relation of multifractal dimensions to critical exponents such as the order parameter exponent $β$ and the correlation length exponent $ν$ is investigated. We discuss a number of scaling relations between spectra of critical exponents, showing that all of the critical exponents necessary to characterize the critical phenomenon can be obtained within the generalized multifractal analysis. Furthermore we show how bounds for the correlation length exponent $ν$ are obtained by the typical order parameter exponent $α_0$ and make contact between the multifractal analysis and the finite size scaling approach in 2-d by relying on conformal mapping arguments.

cond-mat↗
arXiv1993

The Quartet State of the Two-Dimensional Heisenberg Model with Spin 1/2 on a Square Lattice

The low-energy properties of the two-dimensional Heisenberg model with spin-$\frac{1}{2}$ on a square lattice are investigated on the basis of the local dimer order. The lattice is divided into square blocks consisting of the quartet of spins. The spin variables and the Heisenberg Hamiltonian are expressed in terms of the low-energy quartet variables. On the basis of the Dyson-Maleev representation the spin-wave theory of the quartet state is developed. The spectrum of the lower magnon excitations consists of three degenerate modes with the energy gap $Δ=0.17J$. The ground state energy per spin $E/N =-0.6J$. This preprint repeats in the main the previous one but it contains calculations of the basic corrections and therefore has complete character.

cond-mat↗
arXiv1994

Luttinger States at the Edge

An effective wavefunction for the edge excitations in the Fractional quantum Hall effect can be found by dimensionally reducing the bulk wavefunction. Treated this way the Laughlin $ν=1/(2n+1)$ wavefunction yields a Luttinger model ground state. We identify the edge-electron field with a Luttinger hyper-fermion operator, and the edge electron itself with a non-backscattering Bogoliubov quasi-particle. The edge-electron propagator may be calculated directly from the effective wavefunction using the properties of a one-dimensional one-component plasma, provided a prescription is adopted which is sensitive to the extra flux attached to the electrons.

cond-mat↗
arXiv1995

SCHRÖDINGER INVARIANCE IN DISCRETE STOCHASTIC SYSTEMS

Local scale invariance for lattice models is studied using new realizations of the Schrödinger algebra. The two-point function is calculated and it turns out that the result can be reproduced from exact two-point correlation functions evaluated in the stationary state of several simple stochastic models.

cond-mat↗
arXiv1994

Gap Formation Probability of the $α-$ Ensemble

In this paper we employ the continuum approximation of Dyson to determine the asymptotic gap formation probability in the spectrum of $N\times N$ Hermitean random matrices. The associated orthogonal polynomials has weight function, $w(x)=e^{-u(x)},$ where $u(x)=x^α,\;α>0,\;0 1/2$ and depends on $α$ for $0<α<1/2.$

cond-mat↗
arXiv1995

Aspects of ${}^3$He and the Standard Electroweak Model

We describe certain aspects of ${}^3He$ and compare them to related aspects of the standard electroweak model of particle physics. We note various similarities in the order parameter structure, defect structure, interactions with fermions and anomalies in the two systems. Many issues in the condensed matter literature that are often confusing to the particle physics reader and vice versa are clarified.

cond-mat↗