Global Wilson-Fisher fixed points

The Wilson-Fisher fixed point with $O(N)$ universality in three dimensions is studied using the renormalisation group. It is shown how a combination of analytical and numerical techniques determine global fixed point solutions to leading order in the derivative expansion for real or purely imaginary fields with moderate numerical effort. Universal and non-universal quantitites such as scaling exponents and mass ratios are computed, for all $N$, together with local fixed point coordinates, radii of convergence, and parameters which control the asymptotic behaviour of the effective action. We also explain when and why finite-$N$ results do not converge pointwise towards the exact infinite-$N$ limit. In the regime of purely imaginary fields, a new link between singularities of fixed point effective actions and singularities of their counterparts by Polchinski are established. Implications for other theories are indicated.Comment: 28 pages, 10 figures, v2: explanations and refs added, to appear (NPB

An exploratory study of heavy domain wall fermions on the lattice

We report on an exploratory study of domain wall fermions (DWF) as a lattice regularisation for heavy quarks. Within the framework of quenched QCD with the tree-level improved Symanzik gauge action we identify the DWF parameters which minimise discretisation effects. We find the corresponding effective 4$d$ overlap operator to be exponentially local, independent of the quark mass. We determine a maximum bare heavy quark mass of $am_h\approx 0.4$, below which the approximate chiral symmetry and O(a)-improvement of DWF are sustained. This threshold appears to be largely independent of the lattice spacing. Based on these findings, we carried out a detailed scaling study for the heavy-strange meson dispersion relation and decay constant on four ensembles with lattice spacings in the range $2.0-5.7\,\mathrm{GeV}$. We observe very mild $a^2$ scaling towards the continuum limit. Our findings establish a sound basis for heavy DWF in dynamical simulations of lattice QCD with relevance to Standard Model phenomenology.Comment: 23 pages, 8 figure

The decay constants fD{\mathbf{f_D}} and fDs{\mathbf{f_{D_{s}}}} in the continuum limit of Nf=2+1{\mathbf{N_f=2+1}} domain wall lattice QCD

We present results for the decay constants of the $D$ and $D_s$ mesons computed in lattice QCD with $N_f=2+1$ dynamical flavours. The simulations are based on RBC/UKQCD's domain wall ensembles with both physical and unphysical light-quark masses and lattice spacings in the range 0.11--0.07$\,$fm. We employ the domain wall discretisation for all valence quarks. The results in the continuum limit are $f_D=208.7(2.8)_\mathrm{stat}\left(^{+2.1}_{-1.8}\right)_\mathrm{sys}\,\mathrm{MeV}$ and $f_{D_{s}}=246.4(1.3)_\mathrm{stat}\left(^{+1.3}_{-1.9}\right)_\mathrm{sys}\,\mathrm{MeV}$ and $f_{D_s}/f_D=1.1667(77)_\mathrm{stat}\left(^{+57}_{-43}\right)_\mathrm{sys}$. Using these results in a Standard Model analysis we compute the predictions $|V_{cd}|=0.2185(50)_\mathrm{exp}\left(^{+35}_{-37}\right)_\mathrm{lat}$ and $|V_{cs}|=1.011(16)_\mathrm{exp}\left(^{+4}_{-9}\right)_\mathrm{lat}$ for the CKM matrix elements

Commuting quantum transfer matrix approach to intrinsic Fermion system: Correlation length of a spinless Fermion model

The quantum transfer matrix (QTM) approach to integrable lattice Fermion systems is presented. As a simple case we treat the spinless Fermion model with repulsive interaction in critical regime. We derive a set of non-linear integral equations which characterize the free energy and the correlation length of $$ for arbitrary particle density at any finite temperatures. The correlation length is determined by solving the integral equations numerically. Especially in low temperature limit this result agrees with the prediction from conformal field theory (CFT) with high accuracy.Comment: 17 page

Relativistic diffusive motion in random electromagnetic fields

We show that the relativistic dynamics in a Gaussian random electromagnetic field can be approximated by the relativistic diffusion of Schay and Dudley. Lorentz invariant dynamics in the proper time leads to the diffusion in the proper time. The dynamics in the laboratory time gives the diffusive transport equation corresponding to the Juettner equilibrium at the inverse temperature \beta^{-1}=mc^{2}. The diffusion constant is expressed by the field strength correlation function (Kubo's formula).Comment: the version published in JP

Exact thermodynamics of an Extended Hubbard Model of single and paired carriers in competition

By exploiting the technique of Sutherland's species, introduced in \cite{DOMO-RC}, we derive the exact spectrum and partition function of a 1D extended Hubbard model. The model describes a competition between dynamics of single carriers and short-radius pairs, as a function of on-site Coulomb repulsion ($U$) and filling ($\rho$). We provide the temperature dependence of chemical potential, compressibility, local magnetic moment, and specific heat. In particular the latter turns out to exhibit two peaks, both related to `charge' degrees of freedom. Their origin and behavior are analyzed in terms of kinetic and potential energy, both across the metal-insulator transition point and in the strong coupling regime.Comment: 14 pages, 15 eps figure

Thoracic wall reconstruction using both portions of the latissimus dorsi previously divided in the course of posterolateral thoracotomy

Objective: Besides other factors, the choice of reconstructive method for full thickness thoracic wall defects depends on the morbidity of preceding surgical procedures. The pedicled latissimus dorsi flap is a reliable and safe option for reconstruction of the thorax. A posterolateral thoracotomy, however, results in division of the muscle. Both parts of the muscle can be employed to close full thickness defects of the chest wall. The proximal part can be pedicled on the thoracodorsal vessels or the serratus branch; the distal part can be pedicled on paravertebral or intercostal perforators. This retrospective study was undertaken to evaluate the reconstructive potential of both parts of the latissimus dorsi in thoracic wall reconstruction after posterolateral thoracotomy. Methods: Between 1987 and 1999, 36 consecutive patients underwent reconstruction of full-thickness thoracic wall defects with latissimus dorsi-flaps after posterolateral thoracotomies. The defects resulted from infection and open window thoracostomy (n=31), trauma (n=3) and resection of tumours (n=2). The patients' average age was 57 years (range 22-76 years). Twenty-five patients were male, 11 were female. In 31 cases the split latissimus dorsi alone was employed; in five cases additional flaps had to be used due to the size of the defects, additional intrathoracic problems or neighbouring defects. Results: In 34 cases defect closure could be achieved without major complications. Empyema recurred in the pleural cavity in one case and one patient died of septicaemia. The 15 patients who had required a respirator in the preoperative phase could be extubated 4.8 days (average) after thoracic wall reconstruction. Postoperative hospital stay averaged 16 days. Conclusions: Different methods are available for reconstruction of full thickness defects of the thoracic wall. After posterolateral thoracotomy in the surgical treatment of empyema, oncologic surgery and traumatology, the latissimus dorsi muscle still retains some reconstructive potential. Advantages are low additional donor site morbidity and anatomical reliability. As it is located near the site of the defect, there is no need for additional surgical sites or intraoperative repositioning. In our service, the split latissimus dorsi muscle flap has proven to be a valuable and reliable option in thoracic wall reconstructio

Collision Thermalization of Nucleons in Relativistic Heavy-Ion Collisions

We consider a possible mechanism of thermalization of nucleons in relativistic heavy-ion collisions. Our model belongs, to a certain degree, to the transport ones; we investigate the evolution of the system created in nucleus-nucleus collision, but we parametrize this development by the number of collisions of every particle during evolution rather than by the time variable. We based on the assumption that the nucleon momentum transfer after several nucleon-nucleon (-hadron) elastic and inelastic collisions becomes a random quantity driven by a proper distribution. This randomization results in a smearing of the nucleon momenta about their initial values and, as a consequence, in their partial isotropization and thermalization. The trial evaluation is made in the framework of a toy model. We show that the proposed scheme can be used for extraction of the physical information from experimental data on nucleon rapidity distribution.Comment: 13 pages, 8 figure

A simplistic pedagogical formulation of a thermal speed distribution using a relativistic framework

A novel pedagogical technique is presented that can be used in the undergraduate (UG) class to formulate a relativistically extended Kinetic Theory of Gases and thermal speed distribution, while assuming the basic thermal symmetry arguments of the famous Maxwell-Boltzmann distribution as presented at the UG level. The adopted framework can be used by students to understand the physics in a thermally governed system at high temperature and speeds, without having to indulge in high level tensor based mathematics, as has been done by the previous works in the subject. Our approach, a logical extension of that proposed by Maxwell, will first recapitulate what is taught and known in the UG class and then present a methodology inspired from the Maxwell-Boltzmann framework that will help students to understand and derive the physics of relativistic thermal systems. The methodology uses simple tools well known to undergraduates and involves a component of computational techniques that can be used to involve students in this exercise. We have tried to place the current work in a larger perspective in regard to the earlier works done and emphasize on it's simplicity and accessibility to students. Towards the end, interesting implications of the relativistically extended distribution are presented and compared with the Maxwell-Boltzmann results at various temperatures.Comment: 13 pages, 5 figures, Publication accepted in Pramana - Journal of Physics (Indian Academy of Sciences). Revised version has an additional section, discussing previous work on relativistic Kinetic Theory in section 2.1 and comparison with these in section 6. Arguments for formulating a relativistic thermal speed distributions have been enriched and made more clear and categorical in section

Lattice path integral approach to the one-dimensional Kondo model

An integrable Anderson-like impurity model in a correlated host is derived from a gl(2$|$1)-symmetric transfer matrix by means of the Quantum-Inverse-Scattering-Method (QISM). Using the Quantum Transfer Matrix technique, free energy contributions of both the bulk and the impurity are calculated exactly. As a special case, the limit of a localized moment in a free bulk (Kondo limit) is performed in the Hamiltonian and in the free energy. In this case, high- and low-temperature scales are calculated with high accuracy.Comment: 26 pages, 9 figure