2,477 research outputs found
The O(n) model on the annulus
We use Coulomb gas methods to propose an explicit form for the scaling limit
of the partition function of the critical O(n) model on an annulus, with free
boundary conditions, as a function of its modulus. This correctly takes into
account the magnetic charge asymmetry and the decoupling of the null states. It
agrees with an earlier conjecture based on Bethe ansatz and quantum group
symmetry, and with all known results for special values of n. It gives new
formulae for percolation (the probability that a cluster connects the two
opposite boundaries) and for self-avoiding loops (the partition function for a
single loop wrapping non-trivially around the annulus.) The limit n->0 also
gives explicit examples of partition functions in logarithmic conformal field
theory.Comment: 20 pp. v.2: important references added to earlier work, minor typos
correcte
Discretely Holomorphic Parafermions in Lattice Z(N) Models
We construct lattice parafermions - local products of order and disorder
operators - in nearest-neighbor Z(N) models on regular isotropic planar
lattices, and show that they are discretely holomorphic, that is they satisfy
discrete Cauchy-Riemann equations, precisely at the critical
Fateev-Zamolodchikov (FZ) integrable points. We generalize our analysis to
models with anisotropic interactions, showing that, as long as the lattice is
correctly embedded in the plane, such discretely holomorphic parafermions exist
for particular values of the couplings which we identify as the anisotropic FZ
points. These results extend to more general inhomogeneous lattice models as
long as the covering lattice admits a rhombic embedding in the plane.Comment: v2: minor corrections; v3: published version - minor corrections and
reference adde
The Number of Incipient Spanning Clusters in Two-Dimensional Percolation
Using methods of conformal field theory, we conjecture an exact form for the
probability that n distinct clusters span a large rectangle or open cylinder of
aspect ratio k, in the limit when k is large.Comment: 9 pages, LaTeX, 1 eps figure. Additional references and comparison
with existing numerical results include
Critical Exponents near a Random Fractal Boundary
The critical behaviour of correlation functions near a boundary is modified
from that in the bulk. When the boundary is smooth this is known to be
characterised by the surface scaling dimension \xt. We consider the case when
the boundary is a random fractal, specifically a self-avoiding walk or the
frontier of a Brownian walk, in two dimensions, and show that the boundary
scaling behaviour of the correlation function is characterised by a set of
multifractal boundary exponents, given exactly by conformal invariance
arguments to be \lambda_n = 1/48 (\sqrt{1+24n\xt}+11)(\sqrt{1+24n\xt}-1).
This result may be interpreted in terms of a scale-dependent distribution of
opening angles of the fractal boundary: on short distance scales these
are sharply peaked around . Similar arguments give the
multifractal exponents for the case of coupling to a quenched random bulk
geometry.Comment: 13 pages. Comments on relation to results in quenched random bulk
added, and on relation to other recent work. Typos correcte
Frustration of decoherence in -shaped superconducting Josephson networks
We examine the possibility that pertinent impurities in a condensed matter
system may help in designing quantum devices with enhanced coherent behaviors.
For this purpose, we analyze a field theory model describing Y- shaped
superconducting Josephson networks. We show that a new finite coupling stable
infrared fixed point emerges in its phase diagram; we then explicitly evidence
that, when engineered to operate near by this new fixed point, Y-shaped
networks support two-level quantum systems, for which the entanglement with the
environment is frustrated. We briefly address the potential relevance of this
result for engineering finite-size superconducting devices with enhanced
quantum coherence. Our approach uses boundary conformal field theory since it
naturally allows for a field-theoretical treatment of the phase slips
(instantons), describing the quantum tunneling between degenerate levels.Comment: 11 pages, 5 .eps figures; several changes in the presentation and in
the figures, upgraded reference
Boundary conformal fields and Tomita--Takesaki theory
Motivated by formal similarities between the continuum limit of the Ising
model and the Unruh effect, this paper connects the notion of an Ishibashi
state in boundary conformal field theory with the Tomita--Takesaki theory for
operator algebras. A geometrical approach to the definition of Ishibashi states
is presented, and it is shownthat, when normalisable the Ishibashi states are
cyclic separating states, justifying the operator state correspondence. When
the states are not normalisable Tomita--Takesaki theory offers an alternative
approach based on left Hilbert algebras, opening the way to extensions of our
construction and the state-operator correspondence.Comment: plain Te
PERFORMANCE MEASURES: BANDWIDTH VERSUS FIDELITY IN PERFORMANCE MANAGEMENT
Performance is of focal and critical interest in organizations. Despite its criticality, when it comes to human performance there are many questions as to how to best measure and manage performance. One such issue is the breadth of the performance that should be considered. In this paper, we examine the issue of the breadth of performance in terms of measuring and managing performance. Overall, a contingency approach is taken in which the expected benefits and preference for broad or narrow performance measures depend on the type of job (fixed or changeable).bandwidth, fidelity in performance management, performance measures
Reflection Scattering Matrix of the Ising Model in a Random Boundary Magnetic Field
The physical properties induced by a quenched surface magnetic field in the
Ising model are investigated by means of boundary quantum field theory in
replica space. Exact boundary scattering amplitudes are proposed and used to
study the averaged quenched correlation functions.Comment: 37 pages (Latex), including 16 figures, one reference adde
Calogero-Sutherland eigenfunctions with mixed boundary conditions and conformal field theory correlators
We construct certain eigenfunctions of the Calogero-Sutherland hamiltonian
for particles on a circle, with mixed boundary conditions. That is, the
behavior of the eigenfunction, as neighbouring particles collide, depend on the
pair of colliding particles. This behavior is generically a linear combination
of two types of power laws, depending on the statistics of the particles
involved. For fixed ratio of each type at each pair of neighboring particles,
there is an eigenfunction, the ground state, with lowest energy, and there is a
discrete set of eigenstates and eigenvalues, the excited states and the
energies above this ground state. We find the ground state and special excited
states along with their energies in a certain class of mixed boundary
conditions, interpreted as having pairs of neighboring bosons and other
particles being fermions. These particular eigenfunctions are characterised by
the fact that they are in direct correspondence with correlation functions in
boundary conformal field theory. We expect that they have applications to
measures on certain configurations of curves in the statistical O(n) loop
model. The derivation, although completely independent from results of
conformal field theory, uses ideas from the "Coulomb gas" formulation.Comment: 35 pages, 9 figure
Lifshitz-like systems and AdS null deformations
Following arXiv:1005.3291 [hep-th], we discuss certain lightlike deformations
of in Type IIB string theory sourced by a lightlike dilaton
dual to the N=4 super Yang-Mills theory with a lightlike varying
gauge coupling. We argue that in the case where the -direction is
noncompact, these solutions describe anisotropic 3+1-dim Lifshitz-like systems
with a potential in the -direction generated by the lightlike dilaton. We
then describe solutions of this sort with a linear dilaton. This enables a
detailed calculation of 2-point correlation functions of operators dual to bulk
scalars and helps illustrate the spatial structure of these theories. Following
this, we discuss a nongeometric string construction involving a
compactification along the -direction of this linear dilaton system. We
also point out similar IIB axionic solutions. Similar bulk arguments for
-noncompact can be carried out for deformations of in
M-theory.Comment: Latex, 20pgs, 1 eps fig; v2. references added; v3. minor
clarifications added, to appear in PR
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