Central Charge and the Andrews-Bailey Construction

From the equivalence of the bosonic and fermionic representations of finitized characters in conformal field theory, one can extract mathematical objects known as Bailey pairs. Recently Berkovich, McCoy and Schilling have constructed a `generalized' character formula depending on two parameters \ra and $\r2$, using the Bailey pairs of the unitary model $M(p-1,p)$. By taking appropriate limits of these parameters, they were able to obtain the characters of model $M(p,p+1)$, $N=1$ model $SM(p,p+2)$, and the unitary $N=2$ model with central charge $c=3(1-{\frac{2}{p}})$. In this letter we computed the effective central charge associated with this `generalized' character formula using a saddle point method. The result is a simple expression in dilogarithms which interpolates between the central charges of these unitary models.Comment: Latex2e, requires cite.sty package, 13 pages. Additional footnote, citation and reference

Threshold photoelectron photoion coincidence spectroscopy and selected ion flow tube reactions of CHF3: comparison of product branching ratios

The threshold photoelectron and threshold photoelectron photoion coincidence spectra of CHF$_3$ in the range 13.5 – 24.5 eV have been recorded. Ion yields and branching ratios have been determined for the three fragments CF$_3^+$, CHF2$^+$ and CF$^+$. The mean kinetic energy releases into fragment ions involving either C-H or C-F bond cleavage have been measured, and compared with statistical and impulsive models. CHF$_3^+$ behaves in a non-statistical manner characteristic of the small-molecule limit, with the ground electronic state and low-lying excited states of CHF$_3^+$ being largely repulsive along the C-H and C-F coordinates, respectively. The rate coefficients and product ion branching ratios have been measured at 298 K in a selected ion flow tube for the reactions of CHF$_3$ with a large number of gas-phase cations whose recombination energies span the range 6.3 through 21.6 eV. A comparison between the branching ratios from the two experiments, together with an analysis of the threshold photoelectron spectrum of CHF$_3$, shows that long-range charge transfer probably occurs for the Ar$^+$ and F$^+$ atomic ions whose recombination energies lie above ca. 15 eV. Below this energy, the mechanism involves a combination of short-range charge transfer and chemical reactions involving a transition state intermediate

Edge Critical Behaviour of the 2-Dimensional Tri-critical Ising Model

Using previous results from boundary conformal field theory and integrability, a phase diagram is derived for the 2 dimensional Ising model at its bulk tri-critical point as a function of boundary magnetic field and boundary spin-coupling constant. A boundary tri-critical point separates phases where the spins on the boundary are ordered or disordered. In the latter range of coupling constant, there is a non-zero critical field where the magnetization is singular. In the former range, as the temperature is lowered, the boundary undergoes a first order transition while the bulk simultaneously undergoes a second order transition.Comment: 6 pages, RevTex, 3 postscript figure

Epigenetic silencing of tumor suppressor long non-coding RNA <i>BM742401</i> in chronic lymphocytic leukemia

published_or_final_versio

Excited Boundary TBA in the Tricritical Ising Model

By considering the continuum scaling limit of the $A_{4}$ RSOS lattice model of Andrews-Baxter-Forrester with integrable boundaries, we derive excited state TBA equations describing the boundary flows of the tricritical Ising model. Fixing the bulk weights to their critical values, the integrable boundary weights admit a parameter $\xi$ which plays the role of the perturbing boundary field $\phi_{1,3}$ and induces the renormalization group flow between boundary fixed points. The boundary TBA equations determining the RG flows are derived in the $\mathcal{B}_{(1,2)}\to \mathcal{B}_{(2,1)}$ example. The induced map between distinct Virasoro characters of the theory are specified in terms of distribution of zeros of the double row transfer matrix.Comment: Latex, 14 pages - Talk given at the Landau meeting "CFT and Integrable Models", Sept. 2002 - v2: some statements about $\phi_{1,2}$ perturbations correcte

On the Integrable Structure of the Ising Model

Starting from the lattice $A_3$ realization of the Ising model defined on a strip with integrable boundary conditions, the exact spectrum (including excited states) of all the local integrals of motion is derived in the continuum limit by means of TBA techniques. It is also possible to follow the massive flow of this spectrum between the UV $c=1/2$ conformal fixed point and the massive IR theory. The UV expression of the eigenstates of such integrals of motion in terms of Virasoro modes is found to have only rational coefficients and their fermionic representation turns out to be simply related to the quantum numbers describing the spectrum.Comment: 18 pages, no figure

Configurational entropy of basaltic melts in Earth’s mantle

Although geophysical observations of mantle regions that suggest the presence of partial melt have often been interpreted in light of the properties of basaltic liquids erupted at the surface, the seismic and rheological consequences of partial melting in the upper mantle depend instead on the properties of interstitial basaltic melt at elevated pressure. In particular, basaltic melts and glasses display anomalous mechanical softening upon compression up to several GPa, suggesting that the relevant properties of melt are strongly pressure-dependent. A full understanding of such a softening requires study, under compression, of the atomic structure of primitive small-degree basaltic melts at their formation depth, which has proven to be difficult. Here we report multiNMR spectra for a simplified basaltic glass quenched at pressures up to 5 GPa (corresponding to depths down to ∼150 km). These data allow quantification of short-range structural parameters such as the populations of coordination numbers of Al and Si cations and the cation pairs bonded to oxygen atoms. In the model basaltic glass, the fraction of ^([5,6])Al is ∼40% at 5 GPa and decreases to ∼3% at 1 atm. The estimated fraction of nonbridging oxygens at 5 GPa is ∼84% of that at ambient pressure. Together with data on variable glass compositions at 1 atm, these results allow us to quantify how such structural changes increase the configurational entropy of melts with increasing density. We explore how configurational entropy can be used to explain the anomalous mechanical softening of basaltic melts and glasses

Configurational entropy of basaltic melts in Earth’s mantle

Although geophysical observations of mantle regions that suggest the presence of partial melt have often been interpreted in light of the properties of basaltic liquids erupted at the surface, the seismic and rheological consequences of partial melting in the upper mantle depend instead on the properties of interstitial basaltic melt at elevated pressure. In particular, basaltic melts and glasses display anomalous mechanical softening upon compression up to several GPa, suggesting that the relevant properties of melt are strongly pressure-dependent. A full understanding of such a softening requires study, under compression, of the atomic structure of primitive small-degree basaltic melts at their formation depth, which has proven to be difficult. Here we report multiNMR spectra for a simplified basaltic glass quenched at pressures up to 5 GPa (corresponding to depths down to ∼150 km). These data allow quantification of short-range structural parameters such as the populations of coordination numbers of Al and Si cations and the cation pairs bonded to oxygen atoms. In the model basaltic glass, the fraction of ^([5,6])Al is ∼40% at 5 GPa and decreases to ∼3% at 1 atm. The estimated fraction of nonbridging oxygens at 5 GPa is ∼84% of that at ambient pressure. Together with data on variable glass compositions at 1 atm, these results allow us to quantify how such structural changes increase the configurational entropy of melts with increasing density. We explore how configurational entropy can be used to explain the anomalous mechanical softening of basaltic melts and glasses