5 research outputs found
The Critical Exponents of Crystalline Random Surfaces
We report on a high statistics numerical study of the crystalline random
surface model with extrinsic curvature on lattices of up to points. The
critical exponents at the crumpling transition are determined by a number of
methods all of which are shown to agree within estimated errors. The
correlation length exponent is found to be from the
tangent-tangent correlation function whereas we find by assuming
finite size scaling of the specific heat peak and hyperscaling. These results
imply a specific heat exponent ; this is a good fit to the
specific heat on a lattice with a per degree of freedom of 1.7
although the best direct fit to the specific heat data yields a much lower
value of . Our measurements of the normal-normal correlation functions
suggest that the model in the crumpled phase is described by an effective field
theory which deviates from a free field theory only by super-renormalizable
interactions.Comment: 18 pages standard LaTex with EPS figure
From Trees to Galaxies: The Potts Model on a Random Surface
The matrix model of random surfaces with c = inf. has recently been solved
and found to be identical to a random surface coupled to a q-states Potts model
with q = inf. The mean field-like solution exhibits a novel type of tree
structure. The natural question is, down to which--if any--finite values of c
and q does this behavior persist? In this work we develop, for the Potts model,
an expansion in the fluctuations about the q = inf. mean field solution. In the
lowest--cubic--non-trivial order in this expansion the corrections to mean
field theory can be given a nice interpretation in terms of structures (trees
and ``galaxies'') of spin clusters. When q drops below a finite q_c, the
galaxies overwhelm the trees at all temperatures, thus suppressing mean field
behavior. Thereafter the phase diagram resembles that of the Ising model, q=2.Comment: 25 pp. (voodoo PostScript replaced by original LaTeX), NBI-HE-94-2
A scenario for the c>1 barrier in non-critical bosonic strings
The c1 matrix models are analyzed within large N renormalization
group, taking into account touching (or branching) interactions. The c<1
modified matrix model with string exponent gamma>0 is naturally associated with
an unstable fixed point, separating the Liouville phase (gamma<0) from the
branched polymer phase (gamma=1/2). It is argued that at c=1 this multicritical
fixed point and the Liouville fixed point coalesce, and that both fixed points
disappear for c>1. In this picture, the critical behavior of c>1 matrix models
is generically that of branched polymers, but only within a scaling region
which is exponentially small when c -> 1. It also explains the behavior of
multiple Ising spins coupled to gravity. Large crossover effects occur for c-1
small enough, with a c ~ 1 pseudo-scaling which explains numerical results.Comment: 20 pages, REVTeX3.0 + epsf, 10 figures. 1 reference added. To appear
in Nucl. Phys.
The confining string and its breaking in QCD
We point out that the world sheet swept by the confining string in presence
of dynamical quarks can belong to two different phases, depending on the number
of charge species and the quark masses. When it lies in the normal phase (as
opposed to the tearing one) the string breaking is invisible in the Wilson
loop, while is manifest in operators composed of disjoint sources, as observed
in many numerical experiments. We work out an explicit formula for the
correlator of Polyakov loops at finite temperature, which is then compared with
recent lattice data, both in the quenched case and in presence of dynamical
quarks. The analysis in the quenched case shows that the free bosonic string
model describes accurately the data for distances larger than ~ 0.75 fm. In the
unquenched case we derive predictions on the dependence of the static potential
on the temperature which are compatible with the lattice data.Comment: 15 pages, LaTeX with 4 eps figures (included
Extended Gauge Invariance in Geometrical Particle Models and the Geometry of W-Symmetry
We prove that particle models whose action is given by the integrated -th
curvature function over the world line possess gauge invariances. A
geometrical characterization of these symmetries is obtained via Frenet
equations by rephrasing the -th curvature model in in terms of a
standard relativistic particle in . We ``prove by example'' that the
algebra of these infinitesimal gauge invariances is nothing but \W_{n+2},
thus providing a geometrical picture of the \W-symmetry for these models. As
a spin-off of our approach we give a new global invariant for four-dimensional
curves subject to a curvature constraint.Comment: plain TeX (macros included). Slightly modified version published in
Nuc. Phys.