Dynamic instability transitions in 1D driven diffusive flow with nonlocal hopping

One-dimensional directed driven stochastic flow with competing nonlocal and local hopping events has an instability threshold from a populated phase into an empty-road (ER) phase. We implement this in the context of the asymmetric exclusion process. The nonlocal skids promote strong clustering in the stationary populated phase. Such clusters drive the dynamic phase transition and determine its scaling properties. We numerically establish that the instability transition into the ER phase is second order in the regime where the entry point reservoir controls the current and first order in the regime where the bulk is in control. The first order transition originates from a turn-about of the cluster drift velocity. At the critical line, the current remains analytic, the road density vanishes linearly, and fluctuations scale as uncorrelated noise. A self-consistent cluster dynamics analysis explains why these scaling properties remain that simple.Comment: 11 pages, 14 figures (25 eps files); revised as the publised versio

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

Critical Exponents of the Four-State Potts Model

The critical exponents of the four-state Potts model are directly derived from the exact expressions for the latent heat, the spontaneous magnetization, and the correlation length at the transition temperature of the model.Comment: LaTex, 7 page

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

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

Path Crossing Exponents and the External Perimeter in 2D Percolation

2D Percolation path exponents $x^{\cal P}_{\ell}$ describe probabilities for traversals of annuli by $\ell$ non-overlapping paths, each on either occupied or vacant clusters, with at least one of each type. We relate the probabilities rigorously to amplitudes of $O(N=1)$ models whose exponents, believed to be exact, yield $x^{\cal P}_{\ell}=({\ell}^2-1)/12$. This extends to half-integers the Saleur--Duplantier exponents for $k=\ell/2$ clusters, yields the exact fractal dimension of the external cluster perimeter, $D_{EP}=2-x^{\cal P}_3=4/3$, and also explains the absence of narrow gate fjords, as originally found by Grossman and Aharony.Comment: 4 pages, 2 figures (EPSF). Revised presentatio