The periodic sl(2|1) alternating spin chain and its continuum limit as a bulk Logarithmic Conformal Field Theory at c=0

The periodic sl(2|1) alternating spin chain encodes (some of) the properties of hulls of percolation clusters, and is described in the continuum limit by a logarithmic conformal field theory (LCFT) at central charge c=0. This theory corresponds to the strong coupling regime of a sigma model on the complex projective superspace $\mathbb{CP}^{1|1} = \mathrm{U}(2|1) / (\mathrm{U}(1) \times \mathrm{U}(1|1))$, and the spectrum of critical exponents can be obtained exactly. In this paper we push the analysis further, and determine the main representation theoretic (logarithmic) features of this continuum limit by extending to the periodic case the approach of [N. Read and H. Saleur, Nucl. Phys. B 777 316 (2007)]. We first focus on determining the representation theory of the finite size spin chain with respect to the algebra of local energy densities provided by a representation of the affine Temperley-Lieb algebra at fugacity one. We then analyze how these algebraic properties carry over to the continuum limit to deduce the structure of the space of states as a representation over the product of left and right Virasoro algebras. Our main result is the full structure of the vacuum module of the theory, which exhibits Jordan cells of arbitrary rank for the Hamiltonian.Comment: 69pp, 8 fig

Logarithmic observables in critical percolation

Although it has long been known that the proper quantum field theory description of critical percolation involves a logarithmic conformal field theory (LCFT), no direct consequence of this has been observed so far. Representing critical bond percolation as the Q = 1 limit of the Q-state Potts model, and analyzing the underlying S_Q symmetry of the Potts spins, we identify a class of simple observables whose two-point functions scale logarithmically for Q = 1. The logarithm originates from the mixing of the energy operator with a logarithmic partner that we identify as the field that creates two propagating clusters. In d=2 dimensions this agrees with general LCFT results, and in particular the universal prefactor of the logarithm can be computed exactly. We confirm its numerical value by extensive Monte-Carlo simulations.Comment: 11 pages, 2 figures. V2: as publishe

Radiographic preoperative templating of extra-offset cemented THA implants: How reliable is it and how does it affect survival?

SummaryIntroductionSecuring femoral offset should in theory improve hip stability and abductor muscles moment arms. As problems arise mainly in case of originally increased offset (>40mm), a range of extra-offset stems is available; the exact impact in terms of fixation, however, is not known.HypothesisExtra-offset stems should more reliably reestablish original femoral offsets exceeding 40mm than standard femoral components, limiting instability risk without possible adverse effect on fixation.ObjectiveTo compare the ability of five commonly available femoral stem designs to restitute offset exceeding 40mm, and to assess function and cement fixation at a minimum 6 years’ follow-up in a stem conceived to reproduce such offset.Patients and methodsA continuous series of 74 total hip replacements (THR) in hips with increased (>40mm) femoral offset was studied. All underwent preoperative X-ray templating on Imagika™ software to assess offset reproduction by five models of stem: four standard, and one Lubinus SP2™ extra-offset stem. A retrospective clinical and X-ray study was conducted with a minimum 6 years’ follow-up on the Lubinus SP2™ 117° stems used to try to reproduce offset in the 74 THRs.ResultsApart from the increased (>40mm) offset, the cervicodiaphyseal angle was consistently <135°, <130° in 60 femurs (81%) and <125° in 45 (60%). Planning showed the four standard stems to induce (>5mm femoral offset reduction in 50–83% of cases, versus only 25% with the Lubinus SP2™ 117°). All 74 hips received Lubinus SP2™ 117° stems: at a mean 78 months FU (range, 70–94mo), their mean Postel-Merle d’Aubigné score was 17±1.8 (range, 13–18). Five of the 74 THRs underwent surgical revision: three cases of loosening, in which the stem was replaced, and two of instability, without change of stem. Loosening was not related to offset reproduction quality; two of the three cases were due to initial cementing defect, and the third occurred in a femur with previous history of two osteotomies. There were four cases of dislocation (5.4%: two primary, which were not operated on, and two recurrent, managed by acetabular revision), despite good reproduction of the preoperative offset in three of the four cases. Mean 7-year implant survivorship was 95.1% (±4.8).Discussion and conclusionThe anatomic form of the Lubinus™ SP2 117° should in theory provide a uniform cement mantle. Survivorship, however, is less good than for regular offset versions (126° or 135°). On the other hand, it does reproduce anatomy in case of >40mm offset, providing extra offset of more than 51mm. The slightly shorter survivorship requires more long-term surveillance.Level of evidenceLevel IV, retrospective study

Relative entropy and the stability of shocks and contact discontinuities for systems of conservation laws with non BV perturbations

We develop a theory based on relative entropy to show the uniqueness and L^2 stability (up to a translation) of extremal entropic Rankine-Hugoniot discontinuities for systems of conservation laws (typically 1-shocks, n-shocks, 1-contact discontinuities and n-contact discontinuities of large amplitude) among bounded entropic weak solutions having an additional trace property. The existence of a convex entropy is needed. No BV estimate is needed on the weak solutions considered. The theory holds without smallness condition. The assumptions are quite general. For instance, strict hyperbolicity is not needed globally. For fluid mechanics, the theory handles solutions with vacuum.Comment: 29 page

Blood group typing in five Afghan populations in the North Hindu-Kush region: implications for blood transfusion practice.

International audienceBACKGROUND AND OBJECTIVES: Blood incompatibility arises from individual and ethnic differences in red blood cell (RBC) antigen profiles. This underlines the importance of documenting RBC antigen variability in various ethnic groups. Central Asia is an area with a long and complex migratory history. The purpose of this article is to describe key antigen frequencies of Afghan ethnic groups in the Hindu-Kush region of Afghanistan as a basis for improving blood transfusion practices in that area. MATERIALS AND METHODS: The key ABO, Rh and Kell antigens were investigated in five Afghan populations. In order to depict accurately the blood group gene diversity in the area, DNA from eight additional Pakistani populations were included, and the entire sample set screened using two multiplex polymerase chain reactions sensitive for 17 alleles in 10 blood group genetic systems (MNS, Kell, Duffy, Kidd, Cartwright, Dombrock, Indian, Colton, Diego and Landsteiner-Wiener). RESULTS: Phenotype and allele frequencies fell within the ranges observed in Western European and East Asian populations. Occurrence of DI*01, IN*01, LW*07 and FY*02N.01 and prevalence of ABO*B were consistent with migratory history as well as with putative environmental adaptation in the subtropical environment Hindu-Kush region. CONCLUSION: These findings expand the current knowledge about key antigen frequencies. Regarding occurrence of viral markers, further blood transfusion in the region requires rigorous typing

Measurement induced criticality in quasiperiodic modulated random hybrid circuits

We study one-dimensional hybrid quantum circuits perturbed by quenched quasiperiodic (QP) modulations across the measurement-induced phase transition (MIPT). Considering non-Pisot QP structures, characterized by unbounded fluctuations, allows us to tune the wandering exponent $\beta$ to exceed the Luck bound $\nu \ge 1/(1-\beta)$ for the stability of the MIPT where $\nu\cong 4/3$. Via large-scale numerical simulations of random Clifford circuits interleaved with local projective measurements, we find that sufficiently large QP structural fluctuations destabilize the MIPT and induce a flow to a broad family of critical dynamical phase transitions of the infinite QP type that is governed by the wandering exponent, $\beta$. We numerically determine the associated critical properties, including the correlation length exponent consistent with saturating the Luck bound, and a universal activated dynamical scaling with activation exponent $\psi \cong \beta$, finding excellent agreement with the conclusions of real space renormalization group calculations.Comment: 14 pages, 13 figure