17 research outputs found
Ordered phase and scaling in models and the three-state antiferromagnetic Potts model in three dimensions
Based on a Renormalization-Group picture of symmetric models in three
dimensions, we derive a scaling law for the order parameter in the
ordered phase. An existing Monte Carlo calculation on the three-state
antiferromagnetic Potts model, which has the effective symmetry, is shown
to be consistent with the proposed scaling law. It strongly supports the
Renormalization-Group picture that there is a single massive ordered phase,
although an apparently rotationally symmetric region in the intermediate
temperature was observed numerically.Comment: 5 pages in REVTEX, 2 PostScript figure
Vicious walk with a wall, noncolliding meanders, and chiral and Bogoliubov-deGennes random matrices
Spatially and temporally inhomogeneous evolution of one-dimensional vicious
walkers with wall restriction is studied. We show that its continuum version is
equivalent with a noncolliding system of stochastic processes called Brownian
meanders. Here the Brownian meander is a temporally inhomogeneous process
introduced by Yor as a transform of the Bessel process that is a motion of
radial coordinate of the three-dimensional Brownian motion represented in the
spherical coordinates. It is proved that the spatial distribution of vicious
walkers with a wall at the origin can be described by the eigenvalue-statistics
of Gaussian ensembles of Bogoliubov-deGennes Hamiltonians of the mean-field
theory of superconductivity, which have the particle-hole symmetry. We report
that the time evolution of the present stochastic process is fully
characterized by the change of symmetry classes from the type to the type
I in the nonstandard classes of random matrix theory of Altland and
Zirnbauer. The relation between the non-colliding systems of the generalized
meanders of Yor, which are associated with the even-dimensional Bessel
processes, and the chiral random matrix theory is also clarified.Comment: REVTeX4, 16 pages, 4 figures. v2: some additions and correction
Moments of vicious walkers and M\"obius graph expansions
A system of Brownian motions in one-dimension all started from the origin and
conditioned never to collide with each other in a given finite time-interval
is studied. The spatial distribution of such vicious walkers can be
described by using the repulsive eigenvalue-statistics of random Hermitian
matrices and it was shown that the present vicious walker model exhibits a
transition from the Gaussian unitary ensemble (GUE) statistics to the Gaussian
orthogonal ensemble (GOE) statistics as the time is going on from 0 to .
In the present paper, we characterize this GUE-to-GOE transition by presenting
the graphical expansion formula for the moments of positions of vicious
walkers. In the GUE limit , only the ribbon graphs contribute and the
problem is reduced to the classification of orientable surfaces by genus.
Following the time evolution of the vicious walkers, however, the graphs with
twisted ribbons, called M\"obius graphs, increase their contribution to our
expansion formula, and we have to deal with the topology of non-orientable
surfaces. Application of the recent exact result of dynamical correlation
functions yields closed expressions for the coefficients in the M\"obius
expansion using the Stirling numbers of the first kind.Comment: REVTeX4, 11 pages, 1 figure. v.2: calculations of the Green function
and references added. v.3: minor additions and corrections made for
publication in Phys.Rev.
Interfacial adsorption in Potts models on the square lattice
We study the effect of interfacial phenomena in two-dimensional perfect and
random (or disordered) -state Potts models with continuous phase
transitions, using, mainly, Monte Carlo techniques. In particular, for the
total interfacial adsorption, the critical behavior, including corrections to
scaling, are analyzed. The role of randomness is scrutinized. Results are
discussed applying scaling arguments and invoking findings for bulk critical
properties. In all studied cases, i.e., , , and , the spread
of the interfacial adsorption profiles is observed to increase linearly with
the lattice size at the bulk transition point.Comment: 6 pages, 6 eps figures, 1 table, minor corrections, accepted for
publication in Eur. Phys. J.
Ecological Invasion, Roughened Fronts, and a Competitor's Extreme Advance: Integrating Stochastic Spatial-Growth Models
Both community ecology and conservation biology seek further understanding of
factors governing the advance of an invasive species. We model biological
invasion as an individual-based, stochastic process on a two-dimensional
landscape. An ecologically superior invader and a resident species compete for
space preemptively. Our general model includes the basic contact process and a
variant of the Eden model as special cases. We employ the concept of a
"roughened" front to quantify effects of discreteness and stochasticity on
invasion; we emphasize the probability distribution of the front-runner's
relative position. That is, we analyze the location of the most advanced
invader as the extreme deviation about the front's mean position. We find that
a class of models with different assumptions about neighborhood interactions
exhibit universal characteristics. That is, key features of the invasion
dynamics span a class of models, independently of locally detailed demographic
rules. Our results integrate theories of invasive spatial growth and generate
novel hypotheses linking habitat or landscape size (length of the invading
front) to invasion velocity, and to the relative position of the most advanced
invader.Comment: The original publication is available at
www.springerlink.com/content/8528v8563r7u2742
Observation of Events with an Energetic Forward Neutron in Deep Inelastic Scattering at HERA
In deep inelastic neutral current scattering of positrons and protons at the center of mass energy of 300 GeV, we observe, with the ZEUS detector, events with a high energy neutron produced at very small scattering angles with respect to the proton direction. The events constitute a fixed fraction of the deep inelastic, neutral current event sample independent of Bjorken x and Q2 in the range 3 · 10-4 \u3c xBJ \u3c 6 · 10-3 and 10 \u3c Q2 \u3c 100 GeV2