66 research outputs found
Massless Flows I: the sine-Gordon and O(n) models
The massless flow between successive minimal models of conformal field theory
is related to a flow within the sine-Gordon model when the coefficient of the
cosine potential is imaginary. This flow is studied, partly numerically, from
three different points of view. First we work out the expansion close to the
Kosterlitz-Thouless point, and obtain roaming behavior, with the central charge
going up and down in between the UV and IR values of . Next we
analytically continue the Casimir energy of the massive flow (i.e. with real
cosine term). Finally we consider the lattice regularization provided by the
O(n) model in which massive and massless flows correspond to high- and
low-temperature phases. A detailed discussion of the case is then given
using the underlying N=2 supersymmetry, which is spontaneously broken in the
low-temperature phase. The ``index'' \tr F(-1)^F follows from the Painleve
III differential equation, and is shown to have simple poles in this phase.
These poles are interpreted as occuring from level crossing (one-dimensional
phase transitions for polymers). As an application, new exact results for the
connectivity constants of polymer graphs on cylinders are obtained.Comment: 39 pages, 7 uuencoded figures, BUHEP-93-5, USC-93/003, LPM-93-0
Differential equations and duality in massless integrable field theories at zero temperature
Functional relations play a key role in the study of integrable models. We
argue in this paper that for massless field theories at zero temperature, these
relations can in fact be interpreted as monodromy relations. Combined with a
recently discovered duality, this gives a way to bypass the Bethe ansatz, and
compute directly physical quantities as solutions of a linear differential
equation, or as integrals over a hyperelliptic curve. We illustrate these ideas
in details in the case of the theory, and the associated boundary
sine-Gordon model.Comment: 18 pages, harvma
Critical exponents of domain walls in the two-dimensional Potts model
We address the geometrical critical behavior of the two-dimensional Q-state
Potts model in terms of the spin clusters (i.e., connected domains where the
spin takes a constant value). These clusters are different from the usual
Fortuin-Kasteleyn clusters, and are separated by domain walls that can cross
and branch. We develop a transfer matrix technique enabling the formulation and
numerical study of spin clusters even when Q is not an integer. We further
identify geometrically the crossing events which give rise to conformal
correlation functions. This leads to an infinite series of fundamental critical
exponents h_{l_1-l_2,2 l_1}, valid for 0 </- Q </- 4, that describe the
insertion of l_1 thin and l_2 thick domain walls.Comment: 5 pages, 3 figures, 1 tabl
Boundary flows in minimal models
We discuss in this paper the behaviour of minimal models of conformal theory
perturbed by the operator at the boundary. Using the RSOS
restriction of the sine-Gordon model, adapted to the boundary problem, a series
of boundary flows between different set of conformally invariant boundary
conditions are described. Generalizing the "staircase" phenomenon discovered by
Al. Zamolodchikov, we find that an analytic continuation of the boundary
sinh-Gordon model provides a flow interpolation not only between all minimal
models in the bulk, but also between their possible conformal boundary
conditions. In the particular case where the bulk sinh-Gordon coupling is
turned to zero, we obtain a boundary roaming trajectory in the theory
that interpolates between all the possible spin Kondo models.Comment: 13pgs, harvmac, 2 fig
Time correlations in 1D quantum impurity problems
We develop in this letter an analytical approach using form- factors to
compute time dependent correlations in integrable quantum impurity problems. As
an example, we obtain for the first time the frequency dependent conductivity
for the tunneling between the edges in the fractional
quantum Hall effect, and the spectrum of the spin-spin correlation in
the anisotropic Kondo model and equivalently in the double well system of
dissipative quantum mechanics, both at vanishing temperature.Comment: 4 pages, Revtex and 2 figure
Self-duality in quantum impurity problems
We establish the existence of an exact non-perturbative self-duality in a
variety of quantum impurity problems, including the Luttinger liquid or quantum
wire with impurity. The former is realized in the fractional quantum Hall
effect, where the duality interchanges electrons with Laughlin quasiparticles.
We discuss the mathematical structure underlying this property, which bears an
intriguing resemblance with the work of Seiberg and Witten on supersymmetric
non-abelian gauge theory.Comment: 4 page
N=2 Supersymmetry, Painleve III and Exact Scaling Functions in 2D Polymers
We discuss in this paper various aspects of the off-critical model in
two dimensions. We find the ground-state energy conjectured by Zamolodchikov
for the unitary minimal models, and extend the result to some non-unitary
minimal cases. We apply our results to the discussion of scaling functions for
polymers on a cylinder. We show, using the underlying N=2 supersymmetry, that
the scaling function for one non-contractible polymer loop around the cylinder
is simply related to the solution of the Painleve III differential equation. We
also find the ground-state energy for a single polymer on the cylinder. We
check these results by numerically simulating the polymer system. We also
analyze numerically the flow to the dense polymer phase. We find there
surprising results, with a function that is not monotonous and
seems to have a roaming behavior, getting very close to the values 81/70 and
7/10 between its UV and IR values of 1.Comment: 20 pages (with 2 figures included
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