Integrals of Motion for Critical Dense Polymers and Symplectic Fermions

We consider critical dense polymers ${\cal L}(1,2)$. 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

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

Information and Timing in Repeated Partnerships

In a repeated partnership game with imperfect monitoring, we distinguish among the effects of (1) shortening the period over which actions are held fixed, (2) increasing the frequency with which accumulated information is reported, and (3) reducing the amount of discounting of payoffs between successive periods. While reducing the amount of discounting generally improves incentives for cooperation, the other two changes can have the reverse effect. When the game is specified in the customary way with information reported at the end of each period of fixed action, the net effect of shortening the period length can be to destroy all incentives for cooperation, reversing the usual conclusion associated with the Folk Theorem for repeated games. Moreover, when interest rates are low, reducing the frequency of information reporting can greatly enhance the efficiency of equilibrium