67 research outputs found
Higher moments of spin-spin correlation functions for the ferromagnetic random bond Potts model
Using CFT techniques, we compute the disorder-averaged p-th power of the
spin-spin correlation function for the ferromagnetic random bonds Potts model.
We thus generalize the calculation of Dotsenko, Dotsenko and Picco, where the
case p=2 was considered. Perturbative calculations are made up to the second
order in epsilon (epsilon being proportional to the central charge deviation of
the pure model from the Ising model value). The explicit dependence of the
correlation function on gives an upper bound for the validity of the
expansion, which seems to be valid, in the three-states case, only if p-alpha in
final formula
Critical Behavior of Coupled q-state Potts Models under Weak Disorder
We investigate the effect of weak disorder on different coupled -state
Potts models with using two loops renormalisation group. This study
presents new examples of first order transitions driven by randomness. We found
that weak disorder makes the models decouple. Therefore, it appears that no
relations emerge, at a perturbation level, between the disordered -state Potts model and the two disordered , -state Potts models
(), despite their central charges are similar according to recent
numerical investigations. Nevertheless, when two -state Potts models are
considered (), the system remains always driven in a strong coupling
regime, violating apparently the Imry-Wortis argument.Comment: 7 pages + 1 PS figure (Latex
Effect of Random Impurities on Fluctuation-Driven First Order Transitions
We analyse the effect of quenched uncorrelated randomness coupling to the
local energy density of a model consisting of N coupled two-dimensional Ising
models. For N>2 the pure model exhibits a fluctuation-driven first order
transition, characterised by runaway renormalisation group behaviour. We show
that the addition of weak randomness acts to stabilise these flows, in such a
way that the trajectories ultimately flow back towards the pure decoupled Ising
fixed point, with the usual critical exponents alpha=0, nu=1, apart from
logarithmic corrections. We also show by examples that, in higher dimensions,
such transitions may either become continuous or remain first order in the
presence of randomness.Comment: 13 pp., LaTe
Numerical Results For The 2D Random Bond 3-state Potts Model
We present results of a numerical simulation of the 3-state Potts model with
random bond, in two dimension. In particular, we measure the critical exponent
associated to the magnetization and the specific heat. We also compare these
exponents with recent analytical computations.Comment: 9 pages, latex, 3 Postscript figure
On touching random surfaces, two-dimensional quantum gravity and non-critical string theory
A set of physical operators which are responsible for touching interactions
in the framework of c<1 unitary conformal matter coupled to 2D quantum gravity
is found. As a special case the non-critical bosonic strings are considered.
Some analogies with four dimensional quantum gravity are also discussed, e.g.
creation-annihilation operators for baby universes, Coleman mechanism for the
cosmological constant.Comment: 22 pages, Latex2e, 3 figure
Single-channel correlators and residue calculus
Some simple (namely, single-channel) correlation functions involving an
arbitrary number of fields are computed by means of a direct application of the
residue calculus, through partial fraction expansions. Examples are presented
in minimal models and parafermionic conformal theories. A generic factorized
expression is deduced for the corresponding single-channel structure constants.Comment: 25 pages (harvmac); minor corrections and one ref. adde
Genus Zero Correlation Functions in c<1 String Theory
We compute N-point correlation functions of pure vertex operator states(DK
states) for minimal models coupled to gravity. We obtain agreement with the
matrix model results on analytically continuing in the numbers of cosmological
constant operators and matter screening operators. We illustrate this for the
cases of the and models.Comment: 11 pages, LaTeX, IMSc--92/35. (revised) minor changes plus one
reference adde
Conformational Entropy of Compact Polymers
Exact results for the scaling properties of compact polymers on the square
lattice are obtained from an effective field theory. The entropic exponent
\gamma=117/112 is calculated, and a line of fixed points associated with
interacting chains is identified; along this line \gamma varies continuously.
Theoretical results are checked against detailed numerical transfer matrix
calculations, which also yield a precise estimate for the connective constant
\kappa=1.47280(1).Comment: 4 pages, 1 figur
Guest charges in an electrolyte: renormalized charge, long- and short-distance behavior of the electric potential and density profile
We complement a recent exact study by L. Samaj on the properties of a guest
charge immersed in a two-dimensional electrolyte with charges . In
particular, we are interested in the behavior of the density profiles and
electric potential created by the charge and the electrolyte, and in the
determination of the renormalized charge which is obtained from the
long-distance asymptotics of the electric potential. In Samaj's previous work,
exact results for arbitrary coulombic coupling were obtained for a
system where all the charges are points, provided and .
Here, we first focus on the mean field situation which we believe describes
correctly the limit but large. In this limit we can
study the case when the guest charge is a hard disk and its charge is above the
collapse value . We compare our results for the renormalized charge
with the exact predictions and we test on a solid ground some conjectures of
the previous study. Our study shows that the exact formulas obtained by Samaj
for the renormalized charge are not valid for , contrary to a
hypothesis put forward by Samaj. We also determine the short-distance
asymptotics of the density profiles of the coions and counterions near the
guest charge, for arbitrary coulombic coupling. We show that the coion density
profile exhibit a change of behavior if the guest charge becomes large enough
(). This is interpreted as a first step of the counterion
condensation (for large coulombic coupling), the second step taking place at
the usual Manning--Oosawa threshold
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