63,477 research outputs found
Spectral measure of large random Hankel, Markov and Toeplitz matrices
We study the limiting spectral measure of large symmetric random matrices of
linear algebraic structure. For Hankel and Toeplitz matrices generated by
i.i.d. random variables of unit variance, and for symmetric Markov
matrices generated by i.i.d. random variables of zero mean
and unit variance, scaling the eigenvalues by we prove the almost
sure, weak convergence of the spectral measures to universal, nonrandom,
symmetric distributions , and of unbounded
support. The moments of and are the sum of volumes of
solids related to Eulerian numbers, whereas has a bounded smooth
density given by the free convolution of the semicircle and normal densities.
For symmetric Markov matrices generated by i.i.d. random variables
of mean and finite variance, scaling the eigenvalues by
we prove the almost sure, weak convergence of the spectral measures to
the atomic measure at . If , and the fourth moment is finite, we prove
that the spectral norm of scaled by converges
almost surely to 1.Comment: Published at http://dx.doi.org/10.1214/009117905000000495 in the
Annals of Probability (http://www.imstat.org/aop/) by the Institute of
Mathematical Statistics (http://www.imstat.org
Locations of multicritical points for spin glasses on regular lattices
We present an analysis leading to precise locations of the multicritical
points for spin glasses on regular lattices. The conventional technique for
determination of the location of the multicritical point was previously derived
using a hypothesis emerging from duality and the replica method. In the present
study, we propose a systematic technique, by an improved technique, giving more
precise locations of the multicritical points on the square, triangular, and
hexagonal lattices by carefully examining relationship between two partition
functions related with each other by the duality. We can find that the
multicritical points of the Ising model are located at
on the square lattice, where means the probability of ,
at on the triangular lattice, and at on the
hexagonal lattice. These results are in excellent agreement with recent
numerical estimations.Comment: 17pages, this is the published version with some minnor corrections.
Previous title was "Precise locations of multicritical points for spin
glasses on regular lattices
Gyrotropic magnetic effect and the magnetic moment on the Fermi surface
The current density induced in a clean metal by a
slowly-varying magnetic field is formulated as the low-frequency
limit of natural optical activity, or natural gyrotropy. Working with a
multiband Pauli Hamiltonian, we obtain from the Kubo formula a simple
expression for in terms of the
intrinsic magnetic moment (orbital plus spin) of the Bloch electrons on the
Fermi surface. An alternate semiclassical derivation provides an intuitive
picture of the effect, and takes into account the influence of scattering
processes in dirty metals. This "gyrotropic magnetic effect" is fundamentally
different from the chiral magnetic effect driven by the chiral anomaly and
governed by the Berry curvature on the Fermi surface, and the two effects are
compared for a minimal model of a Weyl semimetal. Like the Berry curvature, the
intrinsic magnetic moment should be regarded as a basic ingredient in the
Fermi-liquid description of transport in broken-symmetry metals.Comment: The Supplemental Material can be found at
http://cmt.berkeley.edu/suppl/zhong-arxiv15-suppl.pd
Re-orientation Transition in Molecular Thin Films: Potts Model with Dipolar Interaction
We study the low-temperature behavior and the phase transition of a thin film
by Monte Carlo simulation. The thin film has a simple cubic lattice structure
where each site is occupied by a Potts parameter which indicates the molecular
orientation of the site. We take only three molecular orientations in this
paper which correspond to the 3-state Potts model. The Hamiltonian of the
system includes: (i) the exchange interaction between nearest-neighbor
sites and (ii) the long-range dipolar interaction of amplitude
truncated at a cutoff distance (iii) a single-ion perpendicular
anisotropy of amplitude . We allow between surface spins, and
otherwise. We show that the ground state depends on the the ratio
and . For a single layer, for a given , there is a critical value
below (above) which the ground-state (GS) configuration of molecular axes
is perpendicular (parallel) to the film surface. When the temperature is
increased, a re-orientation transition occurs near : the low- in-plane
ordering undergoes a transition to the perpendicular ordering at a finite ,
below the transition to the paramagnetic phase. The same phenomenon is observed
in the case of a film with a thickness. We show that the surface phase
transition can occur below or above the bulk transition depending on the ratio
. Surface and bulk order parameters as well as other physical quantities
are shown and discussed.Comment: 7 pages, 11 figures, submitted for publicatio
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