Structural phase transition in evolving networks

A network as a substrate for dynamic processes may have its own dynamics. We propose a model for networks which evolve together with diffusing particles through a coupled dynamics, and investigate emerging structural property. The model consists of an undirected weighted network of fixed mean degree and randomly diffusing particles of fixed density. The weight $w$ of an edge increases by the amount of traffics through its connecting nodes or decreases by a constant factor. Edges are removed with the probability $P_{rew.}=1/(1+w)$ and replaced by new ones having $w=0$ at random locations. We find that the model exhibits a structural phase transition between the homogeneous phase characterized by an exponentially decaying degree distribution and the heterogeneous phase characterized by the presence of hubs. The hubs emerge as a consequence of a positive feedback between the particle and the edge dynamics.Comment: 4 pages, 5figure

Finite-size scaling theory for explosive percolation transitions

The finite-size scaling (FSS) theory for continuous phase transitions has been useful in determining the critical behavior from the size dependent behaviors of thermodynamic quantities. When the phase transition is discontinuous, however, FSS approach has not been well established yet. Here, we develop a FSS theory for the explosive percolation transition arising in the Erd\H{o}s and R\'enyi model under the Achlioptas process. A scaling function is derived based on the observed fact that the derivative of the curve of the order parameter at the critical point $t_c$ diverges with system size in a power-law manner, which is different from the conventional one based on the divergence of the correlation length at $t_c$. We show that the susceptibility is also described in the same scaling form. Numerical simulation data for different system sizes are well collapsed on the respective scaling functions.Comment: 5 pages, 5 figure

Defect Formation and Kinetics of Atomic Terrace Merging

Pairs of atomic scale terraces on a single crystal metal surface can be made to merge controllably under suitable conditions to yield steps of double height and width. We study the effect of various physical parameters on the formation of defects in a kinetic model of step doubling. We treat this manifestly non- equilibrium problem by mapping the model onto a 1-D random sequential adsorption problem and solving this analytically. We also do simulations to check the validity of our treatment. We find that our treatment effectively captures the dynamic evolution and the final state of the surface morphology. We show that the number and nature of the defects formed is controlled by a single dimensionless parameter $q$. For $q$ close to one we show that the fraction of defects rises linearly with $\epsilon \equiv 1-q$ as $0.284 \times \epsilon$. We also show that one can arrive at the final state faster and with fewer defects by changing the parameter with time.Comment: 17 pages, 8 figures. To be submitted to Phys. Rev.

Preroughening transitions in a model for Si and Ge (001) type crystal surfaces

The uniaxial structure of Si and Ge (001) facets leads to nontrivial topological properties of steps and hence to interesting equilibrium phase transitions. The disordered flat phase and the preroughening transition can be stabilized without the need for step-step interactions. A model describing this is studied numerically by transfer matrix type finite-size-scaling of interface free energies. Its phase diagram contains a flat, rough, and disordered flat phase, separated by roughening and preroughening transition lines. Our estimate for the location of the multicritical point where the preroughening line merges with the roughening line, predicts that Si and Ge (001) undergo preroughening induced simultaneous deconstruction transitions.Comment: 13 pages, RevTex, 7 Postscript Figures, submitted to J. Phys.

Work distribution for the driven harmonic oscillator with time-dependent strength: Exact solution and slow driving

We study the work distribution of a single particle moving in a harmonic oscillator with time-dependent strength. This simple system has a non-Gaussian work distribution with exponential tails. The time evolution of the corresponding moment generating function is given by two coupled ordinary differential equations that are solved numerically. Based on this result we study the behavior of the work distribution in the limit of slow but finite driving and show that it approaches a Gaussian distribution arbitrarily well

Fine Details of the Nodal Electronic Excitations in Bi2_2Sr2_2CaCu2_2O8+δ_{8+\delta}

Very high energy resolution photoemission experiments on high quality samples of optimally doped Bi$_2$Sr$_2$CaCu$_2$O$_{8+\delta}$ show new features in the low-energy electronic excitations. A marked change in the binding energy and temperature dependence of the near-nodal scattering rates is observed near the superconducting transition temperature, $T_C$. The temperature slope of the scattering rate measured at low energy shows a discontinuity at ~$T_C$. In the superconducting state, coherent excitations are found with the scattering rates showing a cubic dependence on frequency and temperature. The superconducting gap has a d-wave magnitude with negligible contribution from higher harmonics. Further, the bi-layer splitting has been found to be finite at the nodal point.Comment: 5 pages, 4 figure

Extended Universality of the Surface Curvature in Equilibrium Crystal Shapes

We investigate the universal property of curvatures in surface models which display a flat phase and a rough phase whose criticality is described by the Gaussian model. Earlier we derived a relation between the Hessian of the free energy and the Gaussian coupling constant in the six-vertex model. Here we show its validity in a general setting using renormalization group arguments. The general validity of the relation is confirmed numerically in the RSOS model by comparing the Hessian of the free energy and the Gaussian coupling constant in a transfer matrix finite-size-scaling study. The Hessian relation gives clear understanding of the universal curvature jump at roughening transitions and facet edges and also provides an efficient way of locating the phase boundaries.Comment: 19 pages, RevTex, 3 Postscript Figures, To appear in Phys. Rev.