The effect of finite-size and boundary conditions on the I-V characteristics of a resistively shu... more The effect of finite-size and boundary conditions on the I-V characteristics of a resistively shunted, twodimensional Josephson-junction array in zero magnetic field is studied both analytically and numerically. Through a detailed analysis of activation, driven diffusion, and destruction of free vortices under periodic boundary conditions, we obtain a two-scale finite-size scaling expression which, in particular, resolves a previously reported discrepancy between the analytical treatment of Ambegaokar et al. ͓Ambegaokar, Halperin, Nelson, and Siggia, Phys. Rev. Lett. 40, 783 ͑1978͔͒ and numerical simulations. The effect of finite array width on the I-V curves in the experimentally studied open networks is governed by a different, one-scale scaling expression with a different underlying physical mechanism. For arrays of sufficiently large width, data from the two types of boundary conditions provide lower and upper bounds on the asymptotic value of the voltage. Large-scale simulations ͑up to 2304ϫ512 nodes͒ are carried out to verify the phenomenological analysis.
%e consider a one-dimensional system of classical planar spins with nearest-neighbor chiral inter... more %e consider a one-dimensional system of classical planar spins with nearest-neighbor chiral interactions in the presence of a magnetic Seld. The phase diagram of the model at zero temperature is studied with use of the method of e8'ective potentials and other numerical and analytical techniques. In contrast to the Frenkel-Kontorova model, the interaction potential between spins is not strictly convex, and this leads to some qualitatively di8'erent behavior. Among other interesting features, we find a succession of 6rst-order transitions, sequences of triple points and their accumulation points, and points where the ground state is in6nitely degenerate.
We consider the disorder-induced fluctuations of a directed polymer confined between two walls wi... more We consider the disorder-induced fluctuations of a directed polymer confined between two walls with attractive contact potentials. For two-dimensional systems we exploit the mapping to a one-dimensional driven lattice gas with open boundaries to obtain exactly the phase diagram as well as critical exponents and scaling functions characterizing the unbinding transitions. The competition between two attractive walls gives rise to coexistence fluctuations in the bound phase, corresponding to the shock fluctuations in the lattice gas. Scaling arguments are used to generalize these results to higher dimensions and different confinement geometries.
The parity effect in an ultra-small superconducting grain is examined. By applying a generalized ... more The parity effect in an ultra-small superconducting grain is examined. By applying a generalized version of Lieb's spin-reflection positivity technique, we show rigorously that the parity parameter ∆P is nonvanishing in such a system. A positive lower bound for ∆P is derived.
The equilibrium quasicrystal phase of a two-dimensional two-component Lennard-Jones atomic syster... more The equilibrium quasicrystal phase of a two-dimensional two-component Lennard-Jones atomic systern and two different ensembles of random tilings (binary and unconstrained) are analyzed by means of Monte Carlo simulations. We find that the quasicrystal phase in the atomic system is well described by the random-tiling model. Despite the nonzero configurational entropy density, the phason fluctuations are found not to destroy the quasi-long-range translational order in this phase, in agreement with conjectured square-gradient phason elasticity. Nearly identical, temperature-independent, reduced, phason elastic constants are determined in all three cases.
A three-dimensional random-tiling icosahedral quasicrystal is studied by a Monte Carlo simulation... more A three-dimensional random-tiling icosahedral quasicrystal is studied by a Monte Carlo simulation. The hypothesis of long-range positional order in the system is confirmed through analysis of the finitesize scaling behavior of phason fluctuations and Fourier peak intensities. By investigating the diffuse scattering we determine the phason stiffness constants. A finite-size scaling form for the Fourier intensity near an icosahedral reciprocal wave vector is proposed.
The structure of nanoclusters is complex to describe due to their noncrystallinity, even though b... more The structure of nanoclusters is complex to describe due to their noncrystallinity, even though bonding and packing constraints limit the local atomic arrangements to only a few types. A computational scheme is presented to extract coordination motifs from sample atomic configurations. The method is based on a clustering analysis of multipole moments for atoms in the first coodination shell. Its power to capture large-scale structural properties is demonstrated by scanning through the ground state of the Lennard-Jones and C60 clusters collected at the Cambridge Cluster Database.
The Rapid Communications section is intended for the accelerated publication of important new res... more The Rapid Communications section is intended for the accelerated publication of important new results Sinc.e manuscripts submitted to this section are git en priority treatment both in the editorial once and in production, authors should explain in their submittal letter why the work justtftes this special handling A.Rapid Communication should be no longer than 3' printed
The roughening behavior of a moving surface under a deposition and evaporation dynamics is explor... more The roughening behavior of a moving surface under a deposition and evaporation dynamics is explored within the hypercube-stacking model. One limiting case of the model is an equilibrium surface, which exhibits thermal roughening for surface dimension d & 2. Another limiting case is nonequilibrium irreversible growth, where the model is shown to map exactly to zero-temperature directed polymers on a hypercubic lattice with a random energy distribution. Results of exact calculations for d = 1 and of large-scale Monte Carlo simulations [N = 2, 11520, and 2 x 192 surface sites for d = 1, 2, and 3, respectively] are presented that establish the Kardar-Parisi-Zhang equation as the correct continuum description of the growth process. For pure deposition (i.e., irreversible growth), careful analysis of surface width data, yields the exponents P(2) = 0.240 6 0.001 and P(3) = 0.180 6 0.005, which violate a number of recent conjectures. By allowing for evaporation, we observe a less rapid increase of the surface roughness as a function of time. This plienomenon is consistently explained by a crossover scenario for d = 1 and 2 but a nonequilibrium roughening transition for d = 3, as predicted by a perturbative renormalization-group analysis of the Kardar-Parisi-Zhang equation. Detailed predictions on crossover scaling from the renormalizationgroup analysis are also confirmed by simulation data. In the d = 1 case, some of the continuum parameters characterizing the renormalization-group Bow are obtained explicitly in terms of the lattice parameters via the exact calculation of steady-state properties of the model.
The Kardar-Parisi-Zhang equation for surface growth is analyzed in the regime where the nonlinear... more The Kardar-Parisi-Zhang equation for surface growth is analyzed in the regime where the nonlinear coupling constant is small. We present detailed calculations for the mean-square surface width in terms of the bare parameters of the equation. For surface dimension d & 2, this quantity is shown to obey crossover scaling. The case d = 2 is marked by an exponentially slow crossover associated with the marginally unstable character of the linear theory. For d & 2 a renormalization-group analysis in the one-loop approximation yields a logarithmic scaling form at the roughening transition between smooth and rough growth phases. The crossover behavior on either side of this transition is discussed.
A two-dimensional rhombus tiling model with a matching-rule-based energy is analyzed using real-s... more A two-dimensional rhombus tiling model with a matching-rule-based energy is analyzed using real-space renormalization-group methods and Monte Carlo simulations. The model spans a range from T=O quasiperiodic crystal (Penrose tiling) to a random-tiling quasicrystal at high temperatures. A heuristic picture for the disordering of the ground-state quasiperiodicity at low temperatures is proposed and corroborated with exact and renormalization-group calculations of the phason elastic energy, which shows a linear dependence on the strain at T=O but changes to a quadratic behavior at T&0 and sufficiently small strain. This is further supported by the Monte Carlo result that phason fluctuations diverge logarithmically with system size for all T &0, which indicates the presence of quasi-long-range translational order in the system, meaning algebraically decaying correlations. A close connection between the rhombus tiling model and the general surface-roughening phenomena is established. Extension of the results to three dimensions and their possible implication to experimental systems is also addressed.
Waiting-Time Formulation of Surface Growth and Mapping to Directed Polymers in a Random Medium
NATO ASI Series, 1993
One class of growth patterns which have been observed in physical and biological systems is the d... more One class of growth patterns which have been observed in physical and biological systems is the development of a seed into a compact cluster with a rough surface or interface.1 Examples of this type include vacuum-deposited thin films2 at low surface mobility and bacteria colonies3 on an agar plate. Recent theoretical studies4 of the roughness of a moving surface have focused on the analysis and simulation of models with simple kinetic growth rules. Many of these models have been found to exhibit a universal dynamic scale invariance.5 The origin of universality among these models has been elucidated by Kardax, Parisi, and Zhang6 within a continuum theory.
Physica A: Statistical Mechanics and its Applications, 1998
The coarsening dynamics of three-dimensional islands on a growing film is discussed. It is assume... more The coarsening dynamics of three-dimensional islands on a growing film is discussed. It is assumed that the origin of the initial instability of a planar surface is the Ehrlich-Schwoebel step-edge barrier for adatom diffusion. Two mechanisms of coarsening are identified: (i) surface diffusion driven by an uneven distribution of bonding energies, and (ii) mound coalescence driven by random deposition. Semiquantitative estimates of the coarsening time are given in each case. When the surface slope saturates, an asymptotic dynamical exponent z = 4 is obtained.
We extend a continuum model recently proposed by Villain [J. Phys. I (France) 1, 19 (1991)]to stu... more We extend a continuum model recently proposed by Villain [J. Phys. I (France) 1, 19 (1991)]to study equilibrium and nonequilibrium diffusion on a high-symmetry surface under a fluctuating particle beam. Exponents characterizing dynamic scaling in various regimes are derived explicitly in all dimensions, as well as the relevant lengths which separate these regimes. Different surface morphologies are correlated with experimentally accessible parameters such as substrate temperature and deposition rate.
Uploads
Papers by Leihan Tang