High-precision estimate of g4 in the 2D Ising model

We compute the renormalized four-point coupling in the 2d Ising model using transfer-matrix techniques. We greatly reduce the systematic uncertainties which usually affect this type of calculations by using the exact knowledge of several terms in the scaling function of the free energy. Our final result is g4=14.69735(3).Comment: 17 pages, revised version with minor changes, accepted for publication in Journal of Physics

Towards a Relativistic Description of Exotic Meson Decays

This work analyses hadronic decays of exotic mesons, with a focus on the lightest one, the $J^{PC}=1^{-+}$ $\pi_{1}$, in a fully relativistic formalism, and makes comparisons with non-relativistic results. We also discuss Coulomb gauge decays of normal mesons that proceed through their hybrid components. The relativistic spin wave functions of mesons and hybrids are constructed based on unitary representations of the Lorentz group. The radial wave functions are obtained from phenomenological considerations of the mass operator. Fully relativistic results (with Wigner rotations) differ significantly from non-relativistic ones. We also find that the decay channels $\pi_{1}\to\pi b_{1}, \pi f_{1}, KK_{1}$ are favored, in agreement with results obtained using other models.Comment: 14 pages, 7 figure

Exact Eigenfunctions of NN-Body system with Quadratic Pair Potential

We obtain all the exact eigenvalues and the corresponding eigenfunctions of $N$-body Bose and Fermi systems with Quadratic Pair Potentials in one dimension. The originally existed first excited state level is missing in one dimension, which results from the operation of symmetry or antisymmetry of identical particles. In two and higher dimensions, we give all the eigenvalues and the analytical ground state wave functions and the number of degeneracy. Through the comparison with Avinash Khare's results, we have perfected his results.Comment: 7 pages,1 figur

MSRE-PCR for analysis of gene-specific DNA methylation

Abnormal DNA methylation is observed in certain promoters of neoplastic cells, although the likelihood of methylation for each individual promoter varies. Simultaneous analysis of many promoters in the same sample can allow use of statistical methods for identification of neoplasia. Here we describe an assay for such analysis, based on digestion of genomic DNA with methylation-sensitive restriction enzyme and multiplexed PCR with gene-specific primers (MSRE-PCR). MSRE-PCR includes extensive digestion of genomic DNA (uncut fragments cannot be identified by PCR), can be applied to dilute samples (<1 pg/μl), requires limited amount of starting material (42 pg or genomic equivalent of seven cells) and can identify methylation in a heterogeneous mix containing <2% of cells with methylated fragments. When applied to 53 promoters of breast cancer cell lines MCF-7, MDA-MB-231 and T47D, MSRE-PCR correctly identified the methylation status of genes analyzed by other techniques. For selected genes results of MSRE-PCR were confirmed by methylation-specific PCR and bisulfite sequencing. The assay can be configured for any number of desired targets in any user-defined set of genes

Accurate Charge-Dependent Nucleon-Nucleon Potential at Fourth Order of Chiral Perturbation Theory

We present the first nucleon-nucleon potential at next-to-next-to-next-to-leading order (fourth order) of chiral perturbation theory. Charge-dependence is included up to next-to-leading order of the isospin-violation scheme. The accuracy for the reproduction of the NN data below 290 MeV lab. energy is comparable to the one of phenomenological high-precision potentials. Since NN potentials of order three and less are known to be deficient in quantitative terms, the present work shows that the fourth order is necessary and sufficient for a reliable NN potential derived from chiral effective Lagrangians. The new potential provides a promising starting point for exact few-body calculations and microscopic nuclear structure theory (including chiral many-body forces derived on the same footing).Comment: 4 pages Revtex including one figur

Do attractive bosons condense?

Motivated by experiments on bose atoms in traps which have attractive interactions (e.g. ^7Li), we consider two models which may be solved exactly. We construct the ground states subject to the constraint that the system is rotating with angular momentum proportional to the number of atoms. In a conventional system this would lead to quantised vortices; here, for attractive interactions, we find that the angular momentum is absorbed by the centre of mass motion. Moreover, the state is uncondensed and is an example of a `fragmented' condensate discussed by Nozi\`eres and Saint James. The same models with repulsive interactions are fully condensed in the thermodynamic limit.Comment: 4 pages, Latex, RevTe

Centers of Mass and Rotational Kinematics for the Relativistic N-Body Problem in the Rest-Frame Instant Form

In the Wigner-covariant rest-frame instant form of dynamics it is possible to develop a relativistic kinematics for the N-body problem. The Wigner hyperplanes define the intrinsic rest frame and realize the separation of the center-of-mass. Three notions of {\it external} relativistic center of mass can be defined only in terms of the {\it external} Poincar\'e group realization. Inside the Wigner hyperplane, an {\it internal} unfaithful realization of the Poincar\'e group is defined. The three concepts of {\it internal} center of mass weakly {\it coincide} and are eliminated by the rest-frame conditions. An adapted canonical basis of relative variables is found. The invariant mass is the Hamiltonian for the relative motions. In this framework we can introduce the same {\it dynamical body frames}, {\it orientation-shape} variables, {\it spin frame} and {\it canonical spin bases} for the rotational kinematics developed for the non-relativistic N-body problem.Comment: 78 pages, revtex fil

Exact Finite-Size-Scaling Corrections to the Critical Two-Dimensional Ising Model on a Torus

We analyze the finite-size corrections to the energy and specific heat of the critical two-dimensional spin-1/2 Ising model on a torus. We extend the analysis of Ferdinand and Fisher to compute the correction of order L^{-3} to the energy and the corrections of order L^{-2} and L^{-3} to the specific heat. We also obtain general results on the form of the finite-size corrections to these quantities: only integer powers of L^{-1} occur, unmodified by logarithms (except of course for the leading $\log L$ term in the specific heat); and the energy expansion contains only odd powers of L^{-1}. In the specific-heat expansion any power of L^{-1} can appear, but the coefficients of the odd powers are proportional to the corresponding coefficients of the energy expansion.Comment: 26 pages (LaTeX). Self-unpacking file containing the tex file and three macros (indent.sty, eqsection.sty, subeqnarray.sty). Added discussions on the results and new references. Version to be published in J. Phys.

Irrelevant operators in the two-dimensional Ising model

By using conformal-field theory, we classify the possible irrelevant operators for the Ising model on the square and triangular lattices. We analyze the existing results for the free energy and its derivatives and for the correlation length, showing that they are in agreement with the conformal-field theory predictions. Moreover, these results imply that the nonlinear scaling field of the energy-momentum tensor vanishes at the critical point. Several other peculiar cancellations are explained in terms of a number of general conjectures. We show that all existing results on the square and triangular lattice are consistent with the assumption that only nonzero spin operators are present.Comment: 32 pages. Added comments and reference

Shell Model Monte Carlo studies of neutron-rich nuclei in the 1s-0d-1p-0f shells

We demonstrate the feasibility of realistic Shell-Model Monte Carlo (SMMC) calculations spanning multiple major shells, using a realistic interaction whose bad saturation and shell properties have been corrected by a newly developed general prescription. Particular attention is paid to the approximate restoration of translational invariance. The model space consists of the full sd-pf shells. We include in the study some well-known T=0 nuclei and several unstable neutron-rich ones around N=20,28. The results indicate that SMMC can reproduce binding energies, B(E2) transitions, and other observables with an interaction that is practically parameter free. Some interesting insight is gained on the nature of deep correlations. The validity of previous studies is confirmed.Comment: 22 pages + 7 postscript figure