arXiv subjects

Marcel den Nijs

Publications and source records attributed to Marcel den Nijs.

23 records · Page 2Linked to original sources

arXiv1998

Directed Ising type dynamic preroughening transition in one dimensional interfaces

We present a realization of directed Ising (DI) type dynamic absorbing state phase transitions in the context of one-dimensional interfaces, such as the relaxation of a step on a vicinal surface. Under the restriction that particle deposition and evaporation can only take place near existing kinks, the interface relaxes into one of three steady states: rough, perfectly ordered flat (OF) without kinks, or disordered flat (DOF) with randomly placed kinks but in perfect up-down alternating order. A DI type dynamic preroughening transition takes place between the OF and DOF phases. At this critical point the asymptotic time evolution is controlled not only by the DI exponents but also by the initial condition. Information about the correlations in the initial state persists and changes the critical exponents.

cond-mat.stat-mech↗

arXiv1996

Stationary State Skewness in KPZ Type Growth

Stationary states in KPZ type growth have interesting short distance properties. We find that typically they are skewed and lack particle-hole symmetry. E.g., hill-tops are typically flatter than valley bottoms, and all odd moments of the height distribution function are non-zero. Stationary state skewness can be turned on and off in the 1+1 dimensional RSOS model. We construct the exact stationary state for its master equation in a 4 dimensional parameter space. In this state steps are completely uncorrelated. Familiar models such as the Kim-Kosterlitz model lie outside this space, and their stationary states are skewed. We demonstrate using finite size scaling that the skewness diverges with systems size, but such that the skewness operator is irrelevant in 1+1 dimensions, with an exponent $y_{sk}\simeq-1$, and that the KPZ fixed point lies at zero-skewness.

cond-mat.stat-mech↗

arXiv1996

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.

cond-mat.stat-mech↗

arXiv1996

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.

cond-mat↗

arXiv1994

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 $2π/N$ massgap for $N\leq 18$ using the master equation. We predict the structure of the crossover scaling function and confirm numerically that $m_0\simeq 4 (π/N)^2 [1+3u^2(s) N/(2π^2)]^{0.5}$ and $m_1\simeq 2 (π/N)^2 [1+ u^2(s) N/π^2]^{0.5}$, 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.

cond-mat↗