12 research outputs found
Corrections to scaling for percolative conduction: anomalous behavior at small L
Recently Grassberger has shown that the correction to scaling for the
conductance of a bond percolation network on a square lattice is a nonmonotonic
function of the linear lattice dimension with a minimum at , while this
anomalous behavior is not present in the site percolation networks. We perform
a high precision numerical study of the bond percolation random resistor
networks on the square, triangular and honeycomb lattices to further examine
this result. We use the arithmetic, geometric and harmonic means to obtain the
conductance and find that the qualitative behavior does not change: it is not
related to the shape of the conductance distribution for small system sizes. We
show that the anomaly at small L is absent on the triangular and honeycomb
networks. We suggest that the nonmonotonic behavior is an artifact of
approximating the continuous system for which the theory is formulated by a
discrete one which can be simulated on a computer. We show that by slightly
changing the definition of the linear lattice size we can eliminate the minimum
at small L without significantly affecting the large L limit.Comment: 3 pages, 4 figures;slightly expanded, 2 figures added. Accepted for
publishing in Phys. Rev.
Anisotropic Scaling in Layered Aperiodic Ising Systems
The influence of a layered aperiodic modulation of the couplings on the
critical behaviour of the two-dimensional Ising model is studied in the case of
marginal perturbations. The aperiodicity is found to induce anisotropic
scaling. The anisotropy exponent z, given by the sum of the surface
magnetization scaling dimensions, depends continuously on the modulation
amplitude. Thus these systems are scale invariant but not conformally invariant
at the critical point.Comment: 7 pages, 2 eps-figures, Plain TeX and epsf, minor correction
Entanglement entropy of the Q >= 4 quantum Potts chain
The entanglement entropy, , is an indicator of quantum correlations
in the ground state of a many body quantum system. At a second-order quantum
phase-transition point in one dimension generally has a logarithmic
singularity. Here we consider quantum spin chains with a first-order quantum
phase transition, the prototype being the -state quantum Potts chain for
and calculate across the transition point. According to
numerical, density matrix renormalization group results at the first-order
quantum phase transition point shows a jump, which is expected to
vanish for . This jump is calculated in leading order as