Phase Transition in the ABC Model

Recent studies have shown that one-dimensional driven systems can exhibit phase separation even if the dynamics is governed by local rules. The ABC model, which comprises three particle species that diffuse asymmetrically around a ring, shows anomalous coarsening into a phase separated steady state. In the limiting case in which the dynamics is symmetric and the parameter $q$ describing the asymmetry tends to one, no phase separation occurs and the steady state of the system is disordered. In the present work we consider the weak asymmetry regime $q=\exp{(-\beta/N)}$ where $N$ is the system size and study how the disordered state is approached. In the case of equal densities, we find that the system exhibits a second order phase transition at some nonzero $\beta_c$. The value of $\beta_c = 2 \pi \sqrt{3}$ and the optimal profiles can be obtained by writing the exact large deviation functional. For nonequal densities, we write down mean field equations and analyze some of their predictions.Comment: 18 pages, 3 figure

The Exact N-point Generating Function in Polyakov-Burgers Turbulence

We find the exact N-point generating function in Polyakov's approach to Burgers turbulence.Comment: 7 pages,Latex,no figure

Two-component Bose gas in an optical lattice at single-particle filling

The Bose-Hubbard model of a two-fold degenerate Bose gas is studied in an optical lattice with one particle per site and virtual tunneling to empty and doubly-occupied sites. An effective Hamiltonian for this system is derived within a continued-fraction approach. The ground state of the effective model is studied in mean-field approximation for a modulated optical lattice. A dimerized mean-field state gives a Mott insulator whereas the lattice without modulations develops long-range correlated phase fluctuations due to a Goldstone mode. This result is discussed in comparison with the superfluid and the Mott-insulating state of a single-component hard-core Bose.Comment: 11 page

Feynman's Propagator Applied to Network Models of Localization

Network models of dirty electronic systems are mapped onto an interacting field theory of lower dimensionality by intepreting one space dimension as time. This is accomplished via Feynman's interpretation of anti-particles as particles moving backwards in time. The method developed maps calculation of the moments of the Landauer conductance onto calculation of correlation functions of an interacting field theory of bosons and fermions. The resulting field theories are supersymmetric and closely related to the supersymmetric spin-chain representations of network models recently discussed by various authors. As an application of the method, the two-edge Chalker-Coddington model is shown to be Anderson localized, and a delocalization transition in a related two-edge network model (recently discussed by Balents and Fisher) is studied by calculation of the average Landauer conductance.Comment: Latex, 14 pages, 2 fig

Lattice-gas Monte Carlo study of adsorption in pores

A lattice gas model of adsorption inside cylindrical pores is evaluated with Monte Carlo simulations. The model incorporates two kinds of site: (a line of) ``axial'' sites and surrounding ``cylindrical shell'' sites, in ratio 1:7. The adsorption isotherms are calculated in either the grand canonical or canonical ensembles. At low temperature, there occur quasi-transitions that would be genuine thermodynamic transitions in mean-field theory. Comparison between the exact and mean-field theory results for the heat capacity and adsorption isotherms are provided

Ground state non-universality in the random field Ising model

Two attractive and often used ideas, namely universality and the concept of a zero temperature fixed point, are violated in the infinite-range random-field Ising model. In the ground state we show that the exponents can depend continuously on the disorder and so are non-universal. However, we also show that at finite temperature the thermal order parameter exponent one half is restored so that temperature is a relevant variable. The broader implications of these results are discussed.Comment: 4 pages 2 figures, corrected prefactors caused by a missing factor of two in Eq. 2., added a paragraph in conclusions for clarit

Quasiparticle density of states in dirty high-T_c superconductors

We study the density of quasiparticle states of dirty d-wave superconductors. We show the existence of singular corrections to the density of states due to quantum interference effects. We then argue that the density of states actually vanishes in the localized phase as $|E|$ or $E^2$ depending on whether time reversal is a good symmetry or not. We verify this result for systems without time reversal symmetry in one dimension using supersymmetry techniques. This simple, instructive calculation also provides the exact universal scaling function for the density of states for the crossover from ballistic to localized behaviour in one dimension. Above two dimensions, we argue that in contrast to the conventional Anderson localization transition, the density of states has critical singularities which we calculate in a $2+\epsilon$ expansion. We discuss consequences of our results for various experiments on dirty high-$T_c$ materials

Heavy pseudoscalar mesons in a Schwinger-Dyson--Bethe-Salpeter approach

The mass spectrum of heavy pseudoscalar mesons, described as quark-antiquark bound systems, is considered within the Bethe-Salpeter formalism with momentum-dependent masses of the constituents. This dependence is found by solving the Schwinger-Dyson equation for quark propagators in rainbow-ladder approximation. Such an approximation is known to provide both a fast convergence of numerical methods and accurate results for lightest mesons. However, as the meson mass increases, the method becomes less stable and special attention must be devoted to details of numerical means of solving the corresponding equations. We focus on the pseudoscalar sector and show that our numerical scheme describes fairly accurately the $\pi$, $K$, $D$, $D_s$ and $\eta_c$ ground states. Excited states are considered as well. Our calculations are directly related to the future physics programme at FAIR.Comment: 9 pages, 3 figures; Based on materials of the contribution "Relativistic Description of Two- and Three-Body Systems in Nuclear Physics", ECT*, October 19-23, 200

Tensionless structure of glassy phase

We study a class of homogeneous finite-dimensional Ising models which were recently shown to exhibit glassy properties. Monte Carlo simulations of a particular three-dimensional model in this class show that the glassy phase obtained under slow cooling is dominated by large scale excitations whose energy $E_l$ scales with their size $l$ as $E_l\sim l^{\Theta}$ with $\Theta\sim 1.33(5)$. Simulations suggest that in another model of this class, namely the four-spin model, energy is concentrated mainly in linear defects making also in this case domain walls tensionless. Two-dimensinal variants of these models are trivial and energy of excitations scales with the exponent $\Theta=1.05(5)$.Comment: 5 page

Correlation functions in a c=1 boundary conformal field theory

We obtain exact results for correlation functions of primary operators in the two-dimensional conformal field theory of a scalar field interacting with a critical periodic boundary potential. Amplitudes involving arbitrary bulk discrete primary fields are given in terms of SU(2) rotation coefficients while boundary amplitudes involving discrete boundary fields are independent of the boundary interaction. Mixed amplitudes involving both bulk and boundary discrete fields can also be obtained explicitly. Two- and three-point boundary amplitudes involving fields at generic momentum are determined, up to multiplicative constants, by the band spectrum in the open-string sector of the theory.Comment: 33 pages, 6 figure