Quantized Hall Conductance in a Two-Dimensional Periodic Potential

The Hall conductance of a two-dimensional electron gas has been studied in a uniform magnetic field and a periodic substrate potential U. The Kubo formula is written in a form that makes apparent the quantization when the Fermi energy lies in a gap. Explicit expressions have been obtained for the Hall conductance for both large and small U/ℏωc

Preroughening, Diffusion, and Growth of An FCC(111) Surface

Preroughening of close-packed fcc(111) surfaces, found in rare gas solids, is an interesting, but poorly characterized phase transition. We introduce a restricted solid-on-solid model, named FCSOS, which describes it. Using mostly Monte Carlo, we study both statics, including critical behavior and scattering properties, and dynamics, including surface diffusion and growth. In antiphase scattering, it is shown that preroughening will generally show up at most as a dip. Surface growth is predicted to be continuous at preroughening, where surface self-diffusion should also drop. The physical mechanism leading to preroughening on rare gas surfaces is analysed, and identified in the step-step elastic repulsion.Comment: Revtex + uuencoded figures, to appear in Physical Review Letter

Universal amplitude of the free energy density in finite-size scaling: the Potts universality

Using the numerical results of the finite-size scaling study of the q-state Potts model by Bloete and Nightingale, we obtain conjectured expressions for the universal amplitude of the free energy density.Comment: Old paper, for archiving. 4 pages, IOP macr

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

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

Surface Incommensurate Structure in an Anisotropic Model with competing interactions on Semiinfinite Triangular Lattice

An anisotropic spin model on a triangular semiinfinite lattice with ferromagnetic nearest-neighbour interactions and one antiferromagnetic next-nearest-neighbour interaction is investigated by the cluster transfer-matrix method. A phase diagram with antiphase, ferromagnetic, incommensurate, and disordered phase is obtained. The bulk uniaxial incommensurate structure modulated in the direction of the competing interactions is found between the antiphase and the disordered phase. The incommensurate structure near the surface with free and boundary condition is studied at different temperatures. Paramagnetic damping at the surface and enhancement of the incommensurate structure in the subsurface region at high temperatures and a new subsurface incommensurate structure modulated in two directions at low temperatures are found.Comment: 13 pages, plainTex, 11 figures, paper submitted to J. Phys.

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

The continuum limit of the integrable open XYZ spin-1/2 chain

We show that the continuum limit of the integrable XYZ spin-1/2 chain on a half-line gives rise to the boundary sine-Gordon theory using the perturbation method.Comment: 8pages, LaTeX; typos in eq.(11) removed, one in reference correcte

Conformal Anomaly and Critical Exponents of the XY-Ising Model

We use extensive Monte Carlo transfer matrix calculations on infinite strips of widths $L$ up to 30 lattice spacing and a finite-size scaling analysis to obtain critical exponents and conformal anomaly number $c$ for the two-dimensional $XY$-Ising model. This model is expected to describe the critical behavior of a class of systems with simultaneous $U(1)$ and $Z_2$ symmetries of which the fully frustrated $XY$ model is a special case. The effective values obtained for $c$ show a significant decrease with $L$ at different points along the line where the transition to the ordered phase takes place in a single transition. Extrapolations based on power-law corrections give values consistent with $c=3/2$ although larger values can not be ruled out. Critical exponents are obtained more accurately and are consistent with previous Monte Carlo simulations suggesting new critical behavior and with recent calculations for the frustrated $XY$ model.Comment: 33 pages, 13 latex figures, uses RevTeX 3.

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