Reconstructed Rough Growing Interfaces; Ridgeline Trapping of Domain Walls

We investigate whether surface reconstruction order exists in stationary growing states, at all length scales or only below a crossover length, $l_{\rm rec}$. The later would be similar to surface roughness in growing crystal surfaces; below the equilibrium roughening temperature they evolve in a layer-by-layer mode within a crossover length scale $l_{\rm R}$, but are always rough at large length scales. We investigate this issue in the context of KPZ type dynamics and a checker board type reconstruction, using the restricted solid-on-solid model with negative mono-atomic step energies. This is a topology where surface reconstruction order is compatible with surface roughness and where a so-called reconstructed rough phase exists in equilibrium. We find that during growth, reconstruction order is absent in the thermodynamic limit, but exists below a crossover length $l_{\rm rec}>l_{\rm R}$, and that this local order fluctuates critically. Domain walls become trapped at the ridge lines of the rough surface, and thus the reconstruction order fluctuations are slaved to the KPZ dynamics

An exact universal amplitude ratio for percolation

The universal amplitude ratio $\tilde{R}_{\xi}$ for percolation in two dimensions is determined exactly using results for the dilute A model in regime 1, by way of a relationship with the q-state Potts model for q<4.Comment: 5 pages, LaTeX, submitted to J. Phys. A. One paragraph rewritten to correct error

Roughening Induced Deconstruction in (100) Facets of CsCl Type Crystals

The staggered 6-vertex model describes the competition between surface roughening and reconstruction in (100) facets of CsCl type crystals. Its phase diagram does not have the expected generic structure, due to the presence of a fully-packed loop-gas line. We prove that the reconstruction and roughening transitions cannot cross nor merge with this loop-gas line if these degrees of freedom interact weakly. However, our numerical finite size scaling analysis shows that the two critical lines merge along the loop-gas line, with strong coupling scaling properties. The central charge is much larger than 1.5 and roughening takes place at a surface roughness much larger than the conventional universal value. It seems that additional fluctuations become critical simultaneously.Comment: 31 pages, 9 figure

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

Anomalous Roughness in Dimer-Type Surface Growth

We point out how geometric features affect the scaling properties of non-equilibrium dynamic processes, by a model for surface growth where particles can deposit and evaporate only in dimer form, but dissociate on the surface. Pinning valleys (hill tops) develop spontaneously and the surface facets for all growth (evaporation) biases. More intriguingly, the scaling properties of the rough one dimensional equilibrium surface are anomalous. Its width, $W\sim L^\alpha$, diverges with system size $L$, as $\alpha={1/3}$ instead of the conventional universal value $\alpha={1/2}$. This originates from a topological non-local evenness constraint on the surface configurations.Comment: Published version in PR

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.

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

Finite-Size Scaling in Two-dimensional Continuum Percolation Models

We test the universal finite-size scaling of the cluster mass order parameter in two-dimensional (2D) isotropic and directed continuum percolation models below the percolation threshold by computer simulations. We found that the simulation data in the 2D continuum models obey the same scaling expression of mass M to sample size L as generally accepted for isotropic lattice problems, but with a positive sign of the slope in the ln-ln plot of M versus L. Another interesting aspect of the finite-size 2D models is also suggested by plotting the normalized mass in 2D continuum and lattice bond percolation models, versus an effective percolation parameter, independently of the system structure (i.e. lattice or continuum) and of the possible directions allowed for percolation (i.e. isotropic or directed) in regions close to the percolation thresholds. Our study is the first attempt to map the scaling behaviour of the mass for both lattice and continuum model systems into one curve.Comment: 9 pages, Revtex, 2 PostScript 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

Some New Results on Complex-Temperature Singularities in Potts Models on the Square Lattice

We report some new results on the complex-temperature (CT) singularities of $q$-state Potts models on the square lattice. We concentrate on the problematic region $Re(a) < 0$ (where $a=e^K$) in which CT zeros of the partition function are sensitive to finite lattice artifacts. From analyses of low-temperature series expansions for $3 \le q \le 8$, we establish the existence, in this region, of complex-conjugate CT singularities at which the magnetization and susceptibility diverge. From calculations of zeros of the partition function, we obtain evidence consistent with the inference that these singularities occur at endpoints $a_e, \ a_e^*$ of arcs protruding into the (complex-temperature extension of the) FM phase. Exponents for these singularities are determined; e.g., for $q=3$, we find $\beta_e=-0.125(1)$, consistent with $\beta_e=-1/8$. By duality, these results also imply associated arcs extending to the (CT extension of the) symmetric PM phase. Analytic expressions are suggested for the positions of some of these singularities; e.g., for $q=5$, our finding is consistent with the exact value $a_e,a_e^*=2(-1 \mp i)$. Further discussions of complex-temperature phase diagrams are given.Comment: 26 pages, latex, with eight epsf figure