Equilibrium of anchored interfaces with quenched disordered growth

The roughening behavior of a one-dimensional interface fluctuating under quenched disorder growth is examined while keeping an anchored boundary. The latter introduces detailed balance conditions which allows for a thorough analysis of equilibrium aspects at both macroscopic and microscopic scales. It is found that the interface roughens linearly with the substrate size only in the vicinity of special disorder realizations. Otherwise, it remains stiff and tilted.Comment: 6 pages, 3 postscript figure

Magnetic Properties of the Metamagnet Ising Model in a three-dimensional Lattice in a Random and Uniform Field

By employing the Monte Carlo technique we study the behavior of Metamagnet Ising Model in a random field. The phase diagram is obtained by using the algorithm of Glaubr in a cubic lattice of linear size $L$ with values ranging from 16 to 42 and with periodic boundary conditions.Comment: 4 pages, 6 figure

On the Scale-Invariant Distribution of the Diffusion Coefficient for Classical Particles Diffusing in Disordered Media.-

The scaling form of the whole distribution P(D) of the random diffusion coefficient D(x) in a model of classically diffusing particles is investigated. The renormalization group approach above the lower critical dimension d=0 is applied to the distribution P(D) using the n-replica approach. In the annealed approximation (n=1), the inverse gaussian distribution is found to be the stable one under rescaling. This identification is made based on symmetry arguments and subtle relations between this model and that of fluc- tuating interfaces studied by Wallace and Zia. The renormalization-group flow for the ratios between consecutive cumulants shows a regime of pure diffusion for small disorder, in which P(D) goes to delta(D-), and a regime of strong disorder where the cumulants grow infinitely large and the diffusion process is ill defined. The boundary between these two regimes is associated with an unstable fixed-point and a subdiffusive behavior: =Ct**(1-d/2). For the quenched case (n goes to 0) we find that unphysical operators are generated raisng doubts on the renormalizability of this model. Implications to other random systems near their lower critical dimension are discussed.Comment: 21 pages, 1 fig. (not included) Use LaTex twic

Equilibrium roughening transition in a 1D modified sine-Gordon model

We present a modified version of the one-dimensional sine-Gordon that exhibits a thermodynamic, roughening phase transition, in analogy with the 2D usual sine-Gordon model. The model is suited to study the crystalline growth over an impenetrable substrate and to describe the wetting transition of a liquid that forms layers. We use the transfer integral technique to write down the pseudo-Schr\"odinger equation for the model, which allows to obtain some analytical insight, and to compute numerically the free energy from the exact transfer operator. We compare the results with Monte Carlo simulations of the model, finding a perfect agreement between both procedures. We thus establish that the model shows a phase transition between a low temperature flat phase and a high temperature rough one. The fact that the model is one dimensional and that it has a true phase transition makes it an ideal framework for further studies of roughening phase transitions.Comment: 11 pages, 13 figures. Accepted for publication in Physical Review

Au-Ag template stripped pattern for scanning probe investigations of DNA arrays produced by Dip Pen Nanolithography

We report on DNA arrays produced by Dip Pen Nanolithography (DPN) on a novel Au-Ag micro patterned template stripped surface. DNA arrays have been investigated by atomic force microscopy (AFM) and scanning tunnelling microscopy (STM) showing that the patterned template stripped substrate enables easy retrieval of the DPN-functionalized zone with a standard optical microscope permitting a multi-instrument and multi-technique local detection and analysis. Moreover the smooth surface of the Au squares (abput 5-10 angstrom roughness) allows to be sensitive to the hybridization of the oligonucleotide array with label-free target DNA. Our Au-Ag substrates, combining the retrieving capabilities of the patterned surface with the smoothness of the template stripped technique, are candidates for the investigation of DPN nanostructures and for the development of label free detection methods for DNA nanoarrays based on the use of scanning probes.Comment: Langmuir (accepted

Non-perturbative phenomena in the three-dimensional random field Ising model

The systematic approach for the calculations of the non-perturbative contributions to the free energy in the ferromagnetic phase of the random field Ising model is developed. It is demonstrated that such contributions appear due to localized in space instanton-like excitations. It is shown that away from the critical region such instanton solutions are described by the set of the mean-field saddle-point equations for the replica vector order parameter, and these equations can be formally reduced to the only saddle-point equation of the pure system in dimensions (D-2). In the marginal case, D=3, the corresponding non-analytic contribution is computed explicitly. Nature of the phase transition in the three-dimensional random field Ising model is discussed.Comment: 12 page

Roughness Scaling in Cyclical Surface Growth

The scaling behavior of cyclical growth (e.g. cycles of alternating deposition and desorption primary processes) is investigated theoretically and probed experimentally. The scaling approach to kinetic roughening is generalized to cyclical processes by substituting the time by the number of cycles $n$. The roughness is predicted to grow as $n^{\beta}$ where $\beta$ is the cyclical growth exponent. The roughness saturates to a value which scales with the system size $L$ as $L^{\alpha}$, where $\alpha$ is the cyclical roughness exponent. The relations between the cyclical exponents and the corresponding exponents of the primary processes are studied. Exact relations are found for cycles composed of primary linear processes. An approximate renormalization group approach is introduced to analyze non-linear effects in the primary processes. The analytical results are backed by extensive numerical simulations of different pairs of primary processes, both linear and non-linear. Experimentally, silver surfaces are grown by a cyclical process composed of electrodeposition followed by 50% electrodissolution. The roughness is found to increase as a power-law of $n$, consistent with the scaling behavior anticipated theoretically. Potential applications of cyclical scaling include accelerated testing of rechargeable batteries, and improved chemotherapeutic treatment of cancerous tumors

Quantum site percolation on amenable graphs

We consider the quantum site percolation model on graphs with an amenable group action. It consists of a random family of Hamiltonians. Basic spectral properties of these operators are derived: non-randomness of the spectrum and its components, existence of an self-averaging integrated density of states and an associated trace-formula.Comment: 10 pages, LaTeX 2e, to appear in "Applied Mathematics and Scientific Computing", Brijuni, June 23-27, 2003. by Kluwer publisher

Ground-State Roughness of the Disordered Substrate and Flux Line in d=2

We apply optimization algorithms to the problem of finding ground states for crystalline surfaces and flux lines arrays in presence of disorder. The algorithms provide ground states in polynomial time, which provides for a more precise study of the interface widths than from Monte Carlo simulations at finite temperature. Using $d=2$ systems up to size $420^2$, with a minimum of $2 \times 10^3$ realizations at each size, we find very strong evidence for a $\ln^2(L)$ super-rough state at low temperatures.Comment: 10 pages, 3 PS figures, to appear in PR

Super-roughening as a disorder-dominated flat phase

We study the phenomenon of super-roughening found on surfaces growing on disordered substrates. We consider a one-dimensional version of the problem for which the pure, ordered model exhibits a roughening phase transition. Extensive numerical simulations combined with analytical approximations indicate that super-roughening is a regime of asymptotically flat surfaces with non-trivial, rough short-scale features arising from the competition between surface tension and disorder. Based on this evidence and on previous simulations of the two-dimensional Random sine-Gordon model [Sanchez et al., Phys. Rev. E 62, 3219 (2000)], we argue that this scenario is general and explains equally well the hitherto poorly understood two-dimensional case.Comment: 7 pages, 4 figures. Accepted for publication in Europhysics Letter