5,636 research outputs found
Branched Polymers on the Given-Mandelbrot family of fractals
We study the average number A_n per site of the number of different
configurations of a branched polymer of n bonds on the Given-Mandelbrot family
of fractals using exact real-space renormalization. Different members of the
family are characterized by an integer parameter b, b > 1. The fractal
dimension varies from to 2 as b is varied from 2 to infinity. We
find that for all b > 2, A_n varies as , where
and are some constants, and . We determine the
exponent , and the size exponent (average diameter of polymer
varies as ), exactly for all b > 2. This generalizes the earlier results
of Knezevic and Vannimenus for b = 3 [Phys. Rev {\bf B 35} (1987) 4988].Comment: 24 pages, 8 figure
Convex lattice polygons of fixed area with perimeter dependent weights
We study fully convex polygons with a given area, and variable perimeter
length on square and hexagonal lattices. We attach a weight t^m to a convex
polygon of perimeter m and show that the sum of weights of all polygons with a
fixed area s varies as s^{-theta_{conv}} exp[K s^(1/2)] for large s and t less
than a critical threshold t_c, where K is a t-dependent constant, and
theta_{conv} is a critical exponent which does not change with t. We find
theta_{conv} is 1/4 for the square lattice, but -1/4 for the hexagonal lattice.
The reason for this unexpected non-universality of theta_{conv} is traced to
existence of sharp corners in the asymptotic shape of these polygons.Comment: 8 pages, 5 figures, revtex
A Time-Dependent Classical Solution of C=1 String Field Theory and Non-Perturbative Effects
We describe a real-time classical solution of string field theory
written in terms of the phase space density, , of the equivalent
fermion theory. The solution corresponds to tunnelling of a single fermion
above the filled fermi sea and leads to amplitudes that go as \exp(- C/
\gst). We discuss how one can use this technique to describe non-perturbative
effects in the Marinari-Parisi model. We also discuss implications of this type
of solution for the two-dimensional black hole.Comment: 23
Stringy Quantum Effects in 2-Dimensional Black-Hole
We discuss the classical 2-dim. black-hole in the framework of the
non-perturbative formulation (in terms of non-relativistic fermions) of c=1
string field theory. We identify an off-shell operator whose classical equation
of motion is that of tachyon in the classical graviton-dilaton black-hole
background. The black-hole `singularity' is identified with the fermi surface
in the phase space of a single fermion, and as such is a consequence of the
semi-classical approximation. An exact treatment reveals that stringy quantum
effects wash away the classical singularity.Comment: 17p, TIFR/TH/92-63; (v3) tex error correcte
Bethe approximation for a system of hard rigid rods: the random locally tree-like layered lattice
We study the Bethe approximation for a system of long rigid rods of fixed
length k, with only excluded volume interaction. For large enough k, this
system undergoes an isotropic-nematic phase transition as a function of density
of the rods. The Bethe lattice, which is conventionally used to derive the
self-consistent equations in the Bethe approximation, is not suitable for
studying the hard-rods system, as it does not allow a dense packing of rods. We
define a new lattice, called the random locally tree-like layered lattice,
which allows a dense packing of rods, and for which the approximation is exact.
We find that for a 4-coordinated lattice, k-mers with k>=4 undergo a continuous
phase transition. For even coordination number q>=6, the transition exists only
for k >= k_{min}(q), and is first order.Comment: 10 pages, 10 figure
Probing Type I' String Theory Using D0 and D4-Branes
We analyse the velocity-dependent potentials seen by D0 and D4-brane probes
moving in Type I' background for head-on scattering off the fixed planes. We
find that at short distances (compared to string length) the D0-brane probe has
a nontrivial moduli space metric, in agreement with the prediction of Type I'
matrix model; however, at large distances it is modified by massive open
strings to a flat metric, which is consistent with the spacetime equations of
motion of Type I' theory. We discuss the implication of this result for the
matrix model proposal for M-theory. We also find that the nontrivial metric at
short distances in the moduli space action of the D0-brane probe is reflected
in the coefficient of the higher dimensional v^4 term in the D4-brane probe
action.Comment: 12 pages, latex. References added and some typos correcte
Wave Propagation in Stringy Black Hole
We further study the nonperturbative formulation of two-dimensional black
holes. We find a nonlinear differential equation satisfied by the tachyon in
the black hole background. We show that singularities in the tachyon field
configurations are always associated with divergent semiclassical expansions
and are absent in the exact theory. We also discuss how the Euclidian black
hole emerges from an analytically continued fermion theory that corresponds to
the right side up harmonic oscillator potential.Comment: 23p, TIFR-TH-93/05; (v3) tex error correcte
Non-relativistic Fermions, Coadjoint Orbits of \winf\ and String Field Theory at
We apply the method of coadjoint orbits of \winf-algebra to the problem of
non-relativistic fermions in one dimension. This leads to a geometric
formulation of the quantum theory in terms of the quantum phase space
distribution of the fermi fluid. The action has an infinite series expansion in
the string coupling, which to leading order reduces to the previously discussed
geometric action for the classical fermi fluid based on the group of
area-preserving diffeomorphisms. We briefly discuss the strong coupling limit
of the string theory which, unlike the weak coupling regime, does not seem to
admit of a two dimensional space-time picture. Our methods are equally
applicable to interacting fermions in one dimension.Comment: 22 page
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