Pre-logarithmic and logarithmic fields in a sandpile model

We consider the unoriented two-dimensional Abelian sandpile model on the half-plane with open and closed boundary conditions, and relate it to the boundary logarithmic conformal field theory with central charge c=-2. Building on previous results, we first perform a complementary lattice analysis of the operator effecting the change of boundary condition between open and closed, which confirms that this operator is a weight -1/8 boundary primary field, whose fusion agrees with lattice calculations. We then consider the operators corresponding to the unit height variable and to a mass insertion at an isolated site of the upper half plane and compute their one-point functions in presence of a boundary containing the two kinds of boundary conditions. We show that the scaling limit of the mass insertion operator is a weight zero logarithmic field.Comment: 18 pages, 9 figures. v2: minor corrections + added appendi

Quantum critical fluctuations in disordered d-wave superconductors

Quasiparticles in the cuprates appear to be subject to anomalously strong inelastic damping mechanisms. To explain the phenomenon, Sachdev and collaborators recently proposed to couple the system to a critically fluctuating order parameter mode of either id_{xy}- or is-symmetry. Motivated by the observation that the energies relevant for the dynamics of this mode are comparable to the scattering rate induced by even moderate impurity concentrations, we here generalize the approach to the presence of static disorder. In the id-case, we find that the coupling to disorder renders the order parameter dynamics diffusive but otherwise leaves much of the phenomenology observed in the clean case intact. In contrast, the interplay of impurity scattering and order parameter fluctuations of is-symmetry entails the formation of a secondary superconductor transition, with a critical temperature exponentially sensitive to the disorder concentration.Comment: 4 pages, 2 figures include

A selected history of expectation bias in physics

The beliefs of physicists can bias their results towards their expectations in a number of ways. We survey a variety of historical cases of expectation bias in observations, experiments, and calculations.Comment: 6 pages, 2 figure

Conformal field theory correlations in the Abelian sandpile mode

We calculate all multipoint correlation functions of all local bond modifications in the two-dimensional Abelian sandpile model, both at the critical point, and in the model with dissipation. The set of local bond modifications includes, as the most physically interesting case, all weakly allowed cluster variables. The correlation functions show that all local bond modifications have scaling dimension two, and can be written as linear combinations of operators in the central charge -2 logarithmic conformal field theory, in agreement with a form conjectured earlier by Mahieu and Ruelle in Phys. Rev. E 64, 066130 (2001). We find closed form expressions for the coefficients of the operators, and describe methods that allow their rapid calculation. We determine the fields associated with adding or removing bonds, both in the bulk, and along open and closed boundaries; some bond defects have scaling dimension two, while others have scaling dimension four. We also determine the corrections to bulk probabilities for local bond modifications near open and closed boundaries.Comment: 13 pages, 5 figures; referee comments incorporated; Accepted by Phys. Rev.

The para-substituent effect and pH-dependence of the organometallic Baeyer–Villiger oxidation of rhenium–carbon bonds

We studied the Baeyer–Villiger (BV) type oxidation of phenylrhenium trioxide (PTO) by H2O2 in the aqueous phase using Quantum Mechanics (density functional theory with the M06 functional) focusing on how the solution pH and the para-substituent affect the Gibbs free energy surfaces. For both PTO and MTO (methylrhenium trioxide) cases, we find that for pH > 1 the BV pathway having OH− as the leaving group is lower in energy than the one involving simultaneous protonation of hydroxide. We also find that during this organometallic BV oxidation, the migrating phenyl is a nucleophile so that substituting functional groups in the para-position of phenyl with increased electron-donating character lowers the migration barrier, just as in organic BV reactions. However, this substituent effect also pushes electron density to Re, impeding HOO− coordination and slowing down the reaction. This is in direct contrast to the organic analog, in which para-substitution has an insignificant influence on 1,2-addition of peracids. Due to the competition of the two opposing effects and the dependence of the resting state on pH and concentration, the reaction rate of the organometallic BV oxidation is surprisingly unaffected by para-substitution

Higher Order and boundary Scaling Fields in the Abelian Sandpile Model

The Abelian Sandpile Model (ASM) is a paradigm of self-organized criticality (SOC) which is related to $c=-2$ conformal field theory. The conformal fields corresponding to some height clusters have been suggested before. Here we derive the first corrections to such fields, in a field theoretical approach, when the lattice parameter is non-vanishing and consider them in the presence of a boundary.Comment: 7 pages, no figure

Boundary conditions and defect lines in the Abelian sandpile model

We add a defect line of dissipation, or crack, to the Abelian sandpile model. We find that the defect line renormalizes to separate the two-dimensional plane into two half planes with open boundary conditions. We also show that varying the amount of dissipation at a boundary of the Abelian sandpile model does not affect the universality class of the boundary condition. We demonstrate that a universal coefficient associated with height probabilities near the defect can be used to classify boundary conditions.Comment: 8 pages, 1 figure; suggestions from referees incorporated; to be published in Phys. Rev.