14,057 research outputs found
Integrals of Motion for Critical Dense Polymers and Symplectic Fermions
We consider critical dense polymers . We obtain for this model
the eigenvalues of the local integrals of motion of the underlying Conformal
Field Theory by means of Thermodynamic Bethe Ansatz. We give a detailed
description of the relation between this model and Symplectic Fermions
including the indecomposable structure of the transfer matrix. Integrals of
motion are defined directly on the lattice in terms of the Temperley Lieb
Algebra and their eigenvalues are obtained and expressed as an infinite sum of
the eigenvalues of the continuum integrals of motion. An elegant decomposition
of the transfer matrix in terms of a finite number of lattice integrals of
motion is obtained thus providing a reason for their introduction.Comment: 53 pages, version accepted for publishing on JSTA
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Possible crater-based pingos, paleolakes and periglacial landscapes in the high latitudes of Utopia Planitia, Mars
The chemical control of wild radish
Wild radish (Raphanus raphanistrum) and wild turnip (Brassica Tournefortii) occur over a very wide area in Western Australia and are two of the most troublesome weeds of cereal crops. In a period of three years the area sprayed with hormone-like weed-killers for the control of these weeds has increased from experimental proportions to an estimated total of 400,000 acres in one season
Some chemical trials with doublegee
There is no more troublesome weed in Western Australia than doublegee. Besides its competitive and smothering: effect on crop and pasture, the spiny fruits penetrate the hoofs of stock causing: lameness. It is a quick-growing- annual which forms seeds at an early stage of growth and rapidly develops a strong tap-root. Dormant seeds will continue to germinate for a number of years and a succession of germinations often occur in the one season. The seedlings are capable of surviving adverse conditions and making rapid recovery
The effect of Hormone-like herbicides on Dwalganup subterranean clover
herbicides of the hormone-like group including,2,4-D and M.C.P.A. are now being used extensively in Western Australia for selective control of wild radish, wild turnip and mustard in cereal crops. It would be too much to expect however, that all crop and pasture plants are resistant to these chemicals and research into the tolerance of cultivated species is now being undertaken in a number of countries
The tolerance of subterranean clover (Trfolium subterranean L.) to chlorinated phenoxyacetic derivatives
The selective phytocidal properties of certain growth-regulating substances were confirmed when Slade, Templeman and Sexton (1945) found in 1940 that applications of 25 lb. naphthylacetic acid per acre to oats weedy with charlock (Brassica sinapis) killed the weed without causing permanent injury to the crop. Within two years of this work investigators in both England and America had recognised the strong growth-regulatory and herbicidal effects of chlorinated phenoxyacetic derivatives
Solvable Critical Dense Polymers
A lattice model of critical dense polymers is solved exactly for finite
strips. The model is the first member of the principal series of the recently
introduced logarithmic minimal models. The key to the solution is a functional
equation in the form of an inversion identity satisfied by the commuting
double-row transfer matrices. This is established directly in the planar
Temperley-Lieb algebra and holds independently of the space of link states on
which the transfer matrices act. Different sectors are obtained by acting on
link states with s-1 defects where s=1,2,3,... is an extended Kac label. The
bulk and boundary free energies and finite-size corrections are obtained from
the Euler-Maclaurin formula. The eigenvalues of the transfer matrix are
classified by the physical combinatorics of the patterns of zeros in the
complex spectral-parameter plane. This yields a selection rule for the
physically relevant solutions to the inversion identity and explicit finitized
characters for the associated quasi-rational representations. In particular, in
the scaling limit, we confirm the central charge c=-2 and conformal weights
Delta_s=((2-s)^2-1)/8 for s=1,2,3,.... We also discuss a diagrammatic
implementation of fusion and show with examples how indecomposable
representations arise. We examine the structure of these representations and
present a conjecture for the general fusion rules within our framework.Comment: 35 pages, v2: comments and references adde
Wind on the boundary for the Abelian sandpile model
We continue our investigation of the two-dimensional Abelian sandpile model
in terms of a logarithmic conformal field theory with central charge c=-2, by
introducing two new boundary conditions. These have two unusual features: they
carry an intrinsic orientation, and, more strangely, they cannot be imposed
uniformly on a whole boundary (like the edge of a cylinder). They lead to seven
new boundary condition changing fields, some of them being in highest weight
representations (weights -1/8, 0 and 3/8), some others belonging to
indecomposable representations with rank 2 Jordan cells (lowest weights 0 and
1). Their fusion algebra appears to be in full agreement with the fusion rules
conjectured by Gaberdiel and Kausch.Comment: 26 pages, 4 figure
Off-Critical Logarithmic Minimal Models
We consider the integrable minimal models , corresponding
to the perturbation off-criticality, in the {\it logarithmic
limit\,} , where are coprime and the
limit is taken through coprime values of . We view these off-critical
minimal models as the continuum scaling limit of the
Forrester-Baxter Restricted Solid-On-Solid (RSOS) models on the square lattice.
Applying Corner Transfer Matrices to the Forrester-Baxter RSOS models in Regime
III, we argue that taking first the thermodynamic limit and second the {\it
logarithmic limit\,} yields off-critical logarithmic minimal models corresponding to the perturbation of the critical
logarithmic minimal models . Specifically, in accord with the
Kyoto correspondence principle, we show that the logarithmic limit of the
one-dimensional configurational sums yields finitized quasi-rational characters
of the Kac representations of the critical logarithmic minimal models . We also calculate the logarithmic limit of certain off-critical
observables related to One Point Functions and show that the
associated critical exponents
produce all conformal dimensions in the infinitely extended Kac table. The corresponding Kac labels
satisfy . The exponent is obtained from the logarithmic limit of the free energy giving the
conformal dimension for the perturbing field . As befits a non-unitary
theory, some observables diverge at criticality.Comment: 18 pages, 5 figures; version 3 contains amplifications and minor
typographical correction
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