Crossover Scaling Functions in One Dimensional Dynamic Growth Models

The crossover from Edwards-Wilkinson ($s=0$) to KPZ ($s>0$) type growth is studied for the BCSOS model. We calculate the exact numerical values for the $k=0$ and $2\pi/N$ massgap for $N\leq 18$ using the master equation. We predict the structure of the crossover scaling function and confirm numerically that $m_0\simeq 4 (\pi/N)^2 [1+3u^2(s) N/(2\pi^2)]^{0.5}$ and $m_1\simeq 2 (\pi/N)^2 [1+ u^2(s) N/\pi^2]^{0.5}$, with $u(1)=1.03596967$. KPZ type growth is equivalent to a phase transition in meso-scopic metallic rings where attractive interactions destroy the persistent current; and to endpoints of facet-ridges in equilibrium crystal shapes.Comment: 11 pages, TeX, figures upon reques

Crossover from Isotropic to Directed Percolation

Directed percolation is one of the generic universality classes for dynamic processes. We study the crossover from isotropic to directed percolation by representing the combined problem as a random cluster model, with a parameter $r$ controlling the spontaneous birth of new forest fires. We obtain the exact crossover exponent $y_{DP}=y_T-1$ at $r=1$ using Coulomb gas methods in 2D. Isotropic percolation is stable, as is confirmed by numerical finite-size scaling results. For $D \geq 3$, the stability seems to change. An intuitive argument, however, suggests that directed percolation at $r=0$ is unstable and that the scaling properties of forest fires at intermediate values of $r$ are in the same universality class as isotropic percolation, not only in 2D, but in all dimensions.Comment: 4 pages, REVTeX, 4 epsf-emedded postscript figure

Dynamical correlations and quantum phase transition in the quantum Potts model

We present a detailed study of the finite temperature dynamical properties of the quantum Potts model in one dimension.Quasiparticle excitations in this model have internal quantum numbers, and their scattering matrix {\gf deep} in the gapped phases is shown to take a simple {\gf exchange} form in the perturbative regimes. The finite temperature correlation functions in the quantum critical regime are determined using conformal invariance, while {\gf far from the quantum critical point} we compute the decay functions analytically within a semiclassical approach of Sachdev and Damle [K. Damle and S. Sachdev, Phys. Rev. B \textbf{57}, 8307 (1998)]. As a consequence, decay functions exhibit a {\em diffusive character}. {\gf We also provide robust arguments that our semiclassical analysis carries over to very low temperatures even in the vicinity of the quantum phase transition.} Our results are also relevant for quantum rotor models, antiferromagnetic chains, and some spin ladder systems.Comment: 18 PRB pages added correction

Temperature Dependence of Facet Ridges in Crystal Surfaces

The equilibrium crystal shape of a body-centered solid-on-solid (BCSOS) model on a honeycomb lattice is studied numerically. We focus on the facet ridge endpoints (FRE). These points are equivalent to one dimensional KPZ-type growth in the exactly soluble square lattice BCSOS model. In our more general context the transfer matrix is not stochastic at the FRE points, and a more complex structure develops. We observe ridge lines sticking into the rough phase where thesurface orientation jumps inside the rounded part of the crystal. Moreover, the rough-to-faceted edges become first-order with a jump in surface orientation, between the FRE point and Pokrovsky-Talapov (PT) type critical endpoints. The latter display anisotropic scaling with exponent $z=3$ instead of familiar PT value $z=2$.Comment: 12 pages, 19 figure

Vicinal Surfaces and the Calogero-Sutherland Model

A miscut (vicinal) crystal surface can be regarded as an array of meandering but non-crossing steps. Interactions between the steps are shown to induce a faceting transition of the surface between a homogeneous Luttinger liquid state and a low-temperature regime consisting of local step clusters in coexistence with ideal facets. This morphological transition is governed by a hitherto neglected critical line of the well-known Calogero-Sutherland model. Its exact solution yields expressions for measurable quantities that compare favorably with recent experiments on Si surfaces.Comment: 4 pages, revtex, 2 figures (.eps

Disordered Flat Phase and Phase Diagram for Restricted Solid on Solid Models of Fcc(110) Surfaces

We discuss the results of a study of restricted solid-on-solid models for fcc (110) surfaces. These models are simple modifications of the exactly solvable BCSOS model, and are able to describe a $(2\times 1)$ missing-row reconstructed surface as well as an unreconstructed surface. They are studied in two different ways. The first is by mapping the problem onto a quantum spin-1/2 one-dimensional hamiltonian of the Heisenberg type, with competing $S^z_iS^z_j$ couplings. The second is by standard Monte Carlo simulations. We find phase diagrams with the following features, which we believe to be quite generic: (i) two flat, ordered phases (unreconstructed and missing-row reconstructed); a rough, disordered phase; an intermediate disordered flat (DF) phase, characterized by monoatomic steps, whose physics is shown to be akin to that of a dimer spin state. (ii) a transition line from the $(2\times 1)$ reconstructed phase to the DF phase showing exponents which appear to be close, within our numerical accuracy, to the 2D-Ising universality class. (iii) a critical (preroughening) line with variable exponents, separating the unreconstructed phase from the DF phase. Possible signatures and order parameters of the DF phase are investigated.Comment: Revtex (22 pages) + 15 figures (uuencoded file

Condensation of magnons and spinons in a frustrated ladder

Motivated by the ever-increasing experimental effort devoted to the properties of frustrated quantum magnets in a magnetic field, we present a careful and detailed theoretical analysis of a one-dimensional version of this problem, a frustrated ladder with a magnetization plateau at m=1/2. We show that even for purely isotropic Heisenberg interactions, the magnetization curve exhibits a rather complex behavior that can be fully accounted for in terms of simple elementary excitations. The introduction of anisotropic interactions (e.g., Dzyaloshinskii-Moriya interactions) modifies significantly the picture and reveals an essential difference between integer and fractional plateaux. In particular, anisotropic interactions generically open a gap in the region between the plateaux, but we show that this gap closes upon entering fractional plateaux. All of these conclusions, based on analytical arguments, are supported by extensive Density Matrix Renormalization Group calculations.Comment: 15 pages, 15 figures. minor changes in tex

Solitonic excitations in the Haldane phase of a S=1 chain

We study low-lying excitations in the 1D $S=1$ antiferromagnetic valence-bond-solid (VBS) model. In a numerical calculation on finite systems the lowest excitations are found to form a discrete triplet branch, separated from the higher-lying continuum. The dispersion of these triplet excitations can be satisfactorily reproduced by assuming approximate wave functions. These wave functions are shown to correspond to moving hidden domain walls, i.e. to one-soliton excitations.Comment: RevTex 3.0, 24 pages, 2 figures on request by fax or mai

Haldane, Large-D and Intermediate-D States in an S=2 Quantum Spin Chain with On-Site and XXZ Anisotropies

Using mainly numerical methods, we investigate the ground-state phase diagram of the S=2 quantum spin chain described by $H = \sum_j (S_j^x S_{j+1}^x + S_j^y S_{j+1}^y + \Delta S_j^z S_{j+1}^z) + D \sum_j (S_j^z)^2$, where $\Delta$ denotes the $XXZ$ anisotropy parameter of the nearest-neighbor interactions and $D$ the on-site anisotropy parameter. We restrict ourselves to the case with $\Delta \ge 0$ and $D \ge 0$ for simplicity. Each of the phase boundary lines is determined by the level spectroscopy or the phenomenological renormalization analysis of numerical results of exact-diagonalization calculations. The resulting phase diagram on the $\Delta$-$D$ plane consists of four phases; the XY 1 phase, the Haldane/large-$D$ phase, the intermediate-$D$ phase and the N\'eel phase. The remarkable natures of the phase diagram are: (1) the Haldane state and the large-$D$ state belong to the same phase; (2) there exists the intermediate-$D$ phase which was predicted by Oshikawa in 1992; (3) the shape of the phase diagram on the $\Delta$-$D$ plane is different from that believed so far. We note that this is the first report of the observation of the intermediate-$D$ phase