Exact Curie temperature for the Ising model on Archimedean and Laves lattices

Using the Feynman-Vdovichenko combinatorial approach to the two dimensional Ising model, we determine the exact Curie temperature for all two dimensional Archimedean lattices. By means of duality, we extend our results to cover all two dimensional Laves lattices. For those lattices where the exact critical temperatures are not exactly known yet, we compare them with Monte Carlo simulations.Comment: 10 pages, 1 figures, 3 table

On Matrix Superpotential and Three-Component Normal Modes

We consider the supersymmetric quantum mechanics (SUSY QM) with three- component normal modes for the Bogomol'nyi-Prasad-Sommerfield (BPS) states. An explicit form of the SUSY QM matrix superpotential is presented and the corresponding three-component bosonic zero-mode eigenfunction is investigated.Comment: 17 pages, no figure. Paper accepted for publication in Journal of Physics A: Mathematical and Theoretica

Dirac fermions on a disclinated flexible surface

A self-consisting gauge-theory approach to describe Dirac fermions on flexible surfaces with a disclination is formulated. The elastic surfaces are considered as embeddings into R^3 and a disclination is incorporated through a topologically nontrivial gauge field of the local SO(3) group which generates the metric with conical singularity. A smoothing of the conical singularity on flexible surfaces is naturally accounted for by regarding the upper half of two-sheet hyperboloid as an elasticity-induced embedding. The availability of the zero-mode solution to the Dirac equation is analyzed.Comment: 6 page

On fusion algebra of chiral SU(N)kSU(N)_{k} models

We discuss some algebraic setting of chiral $SU(N)_{k}$ models in terms of the statistical dimensions of their fields. In particular, the conformal dimensions and the central charge of the chiral $SU(N)_{k}$ models are calculated from their braid matrices. Futhermore, at level K=2, we present the characteristic polynomials of their fusion matrices in a factored form.Comment: 11 pages, ioplpp

The monoclinic phase of PZT ceramics: Raman and phenomenological theory studies

This work reports on the first Raman detection of the tetragonal to monoclinic phase transition in PZT ceramics near morphotropic phase boundary at low temperatures. The transition is characterized by changes in the frequency of lattice modes with the temperature. The results presented here confirm the previous one recently reported by Noheda et al. using high-resolution synchrotron X-ray powder diffraction technique and dielectric measurements. The stability of the new phase is discussed within the framework of phenomenological Landau-Devonshire Theory.Comment: 6 pages including 4 figures, Latex, submitted to Applied Physics Letter

Laboratory predictors of uphill cycling performance in trained cyclists

This study aimed to assess the relationship between an uphill time-trial (TT) performance and both aerobic and anaerobic parameters obtained from laboratory tests. Fifteen cyclists performed a Wingate anaerobic test, a graded exercise test (GXT) and a field-based 20-min TT with 2.7% mean gradient. After a 5-week non-supervised training period, 10 of them performed a second TT for analysis of pacing reproducibility. Stepwise multiple regressions demonstrated that 91% of TT mean power output variation (W kg-1) could be explained by peak oxygen uptake (ml kg-1.min-1) and the respiratory compensation point (W kg-1), with standardised beta coefficients of 0.64 and 0.39, respectively. The agreement between mean power output and power at respiratory compensation point showed a bias ± random error of 16.2 ± 51.8 W or 5.7 ± 19.7%. One-way repeated-measures analysis of variance revealed a significant effect of the time interval (123.1 ± 8.7; 97.8 ± 1.2 and 94.0 ± 7.2% of mean power output, for epochs 0-2, 2-18 and 18-20 min, respectively; P < 0.001), characterising a positive pacing profile. This study indicates that an uphill, 20-min TT-type performance is correlated to aerobic physiological GXT variables and that cyclists adopt reproducible pacing strategies when they are tested 5 weeks apart (coefficients of variation of 6.3; 1 and 4%, for 0-2, 2-18 and 18-20 min, respectively)

MQCD, ('Barely') G_2 Manifolds and (Orientifold of) a Compact Calabi-Yau

We begin with a discussion on two apparently disconnected topics - one related to nonperturbative superpotential generated from wrapping an M2-brane around a supersymmetric three cycle embedded in a G_2-manifold evaluated by the path-integral inside a path-integral approach of [1], and the other centered around the compact Calabi-Yau CY_3(3,243) expressed as a blow-up of a degree-24 Fermat hypersurface in WCP^4[1,1,2,8,12]. For the former, we compare the results with the ones of Witten on heterotic world-sheet instantons [2]. The subtopics covered in the latter include an N=1 triality between Heterotic, M- and F-theories, evaluation of RP^2-instanton superpotential, Picard-Fuchs equation for the mirror Landau-Ginsburg model corresponding to CY_3(3,243), D=11 supergravity corresponding to M-theory compactified on a `barely' G_2 manifold involving CY_3(3,243) and a conjecture related to the action of antiholomorphic involution on period integrals. We then show an indirect connection between the two topics by showing a connection between each one of the two and Witten's MQCD [3]. As an aside, we show that in the limit of vanishing "\zeta", a complex constant that appears in the Riemann surfaces relevant to definining the boundary conditions for the domain wall in MQCD, the infinite series of [4] used to represent a suitable embedding of a supersymmetric 3-cycle in a G_2-mannifold, can be summed.Comment: 37 pages, LaTex; PARTLY based on talks given at ``Seventh Workshop on QCD" [session on "Strings, Branes and (De-)Construction"], Jan 6-10, 2003, La Cittadelle, Villefranche-sur-Mer, France; Fourth Workshop on ``Gauge Fields and Strings", Feb 25-Mar 1, 2003, Jena, Germany; ``XII Oporto Meeting on Geometry, Topology and Strings", July 17-20, 2003, Oporto, Portugal; "SQS03" - International Workshop on "Supersymmetries and Quantum Symmetries', July 24-29, 2003, JINR, Dubna, Russia; poster presented at ``XIV International Congress on Mathematical Physics", July 28-Aug 2, 2003, Lisbon, Portuga