720 research outputs found
An Exactly Soluble Model of Directed Polymers with Multiple Phase Transitions
Polymer chains with hard-core interaction on a two-dimensional lattice are
modeled by directed random walks. Two models, one with intersecting walks (IW)
and another with non-intersecting walks (NIW) are presented, solved and
compared. The exact solution of the two models, based on a representation using
Grassmann variables, leads, surprisingly, to the same analytic expression for
the polymer density and identical phase diagrams. There are three different
phases as a function of hopping probability and single site monomer occupancy,
with a transition from the dense polymer system to a polymer liquid (A) and a
transition from the liquid to an empty lattice (B). Within the liquid phase
there exists a self-dual line with peculiar properties. The derivative of
polymer density with respect to the single site monomer occupancy diverges at
transitions A and B, but is smooth across and along the self-dual line. The
density-density correlation function along the direction , perpendicular to
the axis of directedness has a power law decay 1/ in the entire liquid
phase, in both models. The difference between the two models shows up only in
the behavior of the correlation function along the self-dual line: it decays
exponentially in the IW model and as 1/ in the NIW model.Comment: 8 pages, plain-TeX, figures available upon reques
Interface Unbinding in Structured Wedges
The unbinding properties of an interface near structured wedges are
investigated by discrete models with short range interactions. The calculations
demonstrate that interface unbinding take place in two stages: ) a
continuous filling--like transition in the pure wedge--like parts of the
structure; ) a conclusive discontinuous unbinding. In 2 an exact
transfer matrix approach allows to extract the whole interface phase diagram
and the precise mechanism at the basis of the phenomenon. The Metropolis Monte
Carlo simulations performed in 3 reveal an analogous behavior. The emerging
scenario allows to shed new light onto the problem of wetting of geometrically
rough walls.Comment: 5 pages, 5 figures, to appear in Phys. Rev.
Ground State Wave Function of the Schr\"odinger Equation in a Time-Periodic Potential
Using a generalized transfer matrix method we exactly solve the Schr\"odinger
equation in a time periodic potential, with discretized Euclidean space-time.
The ground state wave function propagates in space and time with an oscillating
soliton-like wave packet and the wave front is wedge shaped. In a statistical
mechanics framework our solution represents the partition sum of a directed
polymer subjected to a potential layer with alternating (attractive and
repulsive) pinning centers.Comment: 11 Pages in LaTeX. A set of 2 PostScript figures available upon
request at [email protected] . Physical Review Letter
Finite Temperature Depinning of a Flux Line from a Nonuniform Columnar Defect
A flux line in a Type-II superconductor with a single nonuniform columnar
defect is studied by a perturbative diagrammatic expansion around an annealed
approximation. The system undergoes a finite temperature depinning transition
for the (rather unphysical) on-the-average repulsive columnar defect, provided
that the fluctuations along the axis are sufficiently large to cause some
portions of the column to become attractive. The perturbative expansion is
convergent throughout the weak pinning regime and becomes exact as the
depinning transition is approached, providing an exact determination of the
depinning temperature and the divergence of the localization length.Comment: RevTeX, 4 pages, 3 EPS figures embedded with epsf.st
A monopole solution from noncommutative multi-instantons
We extend the relation between instanton and monopole solutions of the
selfduality equations in SU(2) gauge theory to noncommutative space-times.
Using this approach and starting from a noncommutative multi-instanton solution
we construct a U(2) monopole configuration which lives in 3 dimensional
ordinary space. This configuration resembles the Wu-Yang monopole and satisfies
the selfduality (Bogomol'nyi) equations for a U(2) Yang-Mills-Higgs system.Comment: 19 pages; title and abstract changed, brane interpretation corrected.
Version to appear in JHE
Kinetic Monte Carlo and Cellular Particle Dynamics Simulations of Multicellular Systems
Computer modeling of multicellular systems has been a valuable tool for
interpreting and guiding in vitro experiments relevant to embryonic
morphogenesis, tumor growth, angiogenesis and, lately, structure formation
following the printing of cell aggregates as bioink particles. Computer
simulations based on Metropolis Monte Carlo (MMC) algorithms were successful in
explaining and predicting the resulting stationary structures (corresponding to
the lowest adhesion energy state). Here we present two alternatives to the MMC
approach for modeling cellular motion and self-assembly: (1) a kinetic Monte
Carlo (KMC), and (2) a cellular particle dynamics (CPD) method. Unlike MMC,
both KMC and CPD methods are capable of simulating the dynamics of the cellular
system in real time. In the KMC approach a transition rate is associated with
possible rearrangements of the cellular system, and the corresponding time
evolution is expressed in terms of these rates. In the CPD approach cells are
modeled as interacting cellular particles (CPs) and the time evolution of the
multicellular system is determined by integrating the equations of motion of
all CPs. The KMC and CPD methods are tested and compared by simulating two
experimentally well known phenomena: (1) cell-sorting within an aggregate
formed by two types of cells with different adhesivities, and (2) fusion of two
spherical aggregates of living cells.Comment: 11 pages, 7 figures; submitted to Phys Rev
Equilibrium of anchored interfaces with quenched disordered growth
The roughening behavior of a one-dimensional interface fluctuating under
quenched disorder growth is examined while keeping an anchored boundary. The
latter introduces detailed balance conditions which allows for a thorough
analysis of equilibrium aspects at both macroscopic and microscopic scales. It
is found that the interface roughens linearly with the substrate size only in
the vicinity of special disorder realizations. Otherwise, it remains stiff and
tilted.Comment: 6 pages, 3 postscript figure
Multigrid Monte Carlo with higher cycles in the Sine Gordon model
We study the dynamical critical behavior of multigrid Monte Carlo for the two
dimensional Sine Gordon model on lattices up to 128 x 128. Using piecewise
constant interpolation, we perform a W-cycle (gamma=2). We examine whether one
can reduce critical slowing down caused by decreasing acceptance rates on large
blocks by doing more work on coarser lattices. To this end, we choose a higher
cycle with gamma = 4. The results clearly demonstrate that critical slowing
down is not reduced in either case.Comment: 7 pages, 1 figure, whole paper including figure contained in ps-file,
DESY 93-00
Universal Asymptotic Statistics of Maximal Relative Height in One-dimensional Solid-on-solid Models
We study the probability density function of the maximum relative
height in a wide class of one-dimensional solid-on-solid models of finite
size . For all these lattice models, in the large limit, a central limit
argument shows that, for periodic boundary conditions, takes a
universal scaling form , with the width of the fluctuating interface and the Airy
distribution function. For one instance of these models, corresponding to the
extremely anisotropic Ising model in two dimensions, this result is obtained by
an exact computation using transfer matrix technique, valid for any .
These arguments and exact analytical calculations are supported by numerical
simulations, which show in addition that the subleading scaling function is
also universal, up to a non universal amplitude, and simply given by the
derivative of the Airy distribution function .Comment: 13 pages, 4 figure
Soft Supersymmetry Breaking due to Dimensional Reduction over Non-Symmetric Coset Spaces
A ten-dimensional supersymmetric gauge theory is compactified over
six-dimensional coset spaces, establishing further our earlier conjecture that
the resulting four dimensional theory is a softly broken supersymmetric gauge
theory in the case that the used coset space is non-symmetric. The specific
non-symmetric six-dimensional spaces examined in the present study are
and .Comment: 14 pages, Latex, Comments related to the Scherk-Schwarz mechanism and
relevant references adde
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