31 research outputs found
Profile and scaling of the fractal exponent of percolations in complex networks
We propose a novel finite size scaling analysis for percolation transition
observed in complex networks. While it is known that cooperative systems in
growing networks often undergo an infinite order transition with inverted
Berezinskii-Kosterlitz-Thouless singularity, it is very hard for numerical
simulations to determine the transition point precisely. Since the neighbor of
the ordered phase is not a simple disordered phase but a critical phase,
conventional finite size scaling technique does not work. In our finite size
scaling, the forms of the scaling functions for the order parameter and the
fractal exponent determine the transition point and critical exponents
numerically for an infinite order transition as well as a standard second order
transition. We confirm the validity of our scaling hypothesis through
Monte-Carlo simulations for bond percolations in some network models: the
decorated (2,2)-flower and the random attachment growing network, where an
infinite order transition occurs, and the configuration model, where a second
order transition occurs.Comment: 6 page
Dynamical Study of Polydisperse Hard-Sphere System
We study the interplay between the fluid-crystal transition and the glass
transition of elastic sphere system with polydispersity using nonequilibrium
molecular dynamics simulations. It is found that the end point of the
crystal-fluid transition line, which corresponds to the critical polydispersity
above which the crystal state is unstable, is on the glass transition line.
This means that crystal and fluid states at the melting point becomes less
distinguishable as polydispersity increases and finally they become identical
state, i.e., marginal glass state, at critical polydispersity.Comment: 5 pages, 5 figure
Nonequilibrium relaxation analysis of a quasi-one-dimensional frustrated XY model for charge-density waves in ring-shaped crystals
We propose a model for charge density waves in ring shaped crystals, which
depicts frustration between intra- and inter-chain couplings coming from
cylindrical bending. It is then mapped to a three dimensional uniformly
frustrated XY model with one dimensional anisotropy in connectivity. The
nonequilibrium relaxation dynamics is investigated by Monte Carlo simulations
to find a phase transition which is quite different from that of usual whisker
crystal. We also find that the low temperature state is a three dimensional
phase vortex lattice with a two dimensional phase coherence in a cylindrical
shell and the system shows power law relaxation in the ordered phase.Comment: 6 pages, 6 epsfiles, revised versio