Finite-temperature-directed polymer in random potentials is described by a transfer matrix method. On 4+1 dimensions, the evidence for a finite-temperature phase transition is found at Tc≈0.18, where the free energy fluctuation grows logarithmically as a function of time t. When T⪡Tc, the...

We develop a phenomenological mapping between submonolayer polynuclear growth (PNG) and the interface dynamics at and below the depinning transition in the Kardar–Parisi–Zhang equation for a negative non-linearity λ. This is possible since the phase transition is of first order, with no...

We generate optimal paths between two given sites on a lattice representing a disordered energy landscape by applying the Dijkstra algorithm. We study the geometrical and energetic scaling properties of the optimal path under two different energy distributions that yield the weak and strong...

The forced and overdamped motion of non-interacting particles in a periodic asymmetric potential is studied. The analysis is focused on synchronization of the motion of the particles with the external sinusoidal driving force. Two cases are considered: a perfect lattice without disorder and a...

We study the non-directed polymer model (NDP model) in the framework of a non-linear growth equation of Burgers type [Kardar–Parisi–Zhang equation with quenched noise (KPZQN equation)] by means of path integrals. The scaling exponents for the KPZQN equation are expressed in terms of the NDP...

The deterministic variant of the Kardar–Parisi–Zhang equation for the evolution of a growing interface is used to model patterning produced by successive laminations in certain stromatolites. Algebraic solutions of the model together with numerical simulations are employed to fit model...

We investigate the time evolution of the roughness of Kadar–Parisi–Zhang (KPZ) equation in (2+1) dimensions. Scaling behavior of the roughness is analyzed from scale transformations and the scaling function is obtained from numerical simulations.

In this paper, a mode of using the Dynamic Renormalization Group (DRG) method is suggested in order to cope with inconsistent results obtained when applying it to a continuous family of one-dimensional nonlocal models. The key observation is that the correct fixed-point dynamical system has to...

In order to estimate roughness exponents of interface growth models, we propose the calculation of effective exponents from the roughness fluctuation σ in the steady state. We compare the finite-size behavior of these exponents and the ones calculated from the average roughness 〈w2〉 for two...