Asymptotic behavior of the finite-size magnetization as a function of the speed of approach to criticality

The main focus of this paper is to determine whether the thermodynamic magnetization is a physically relevant estimator of the finite-size magnetization. This is done by comparing the asymptotic behaviors of these two quantities along parameter sequences converging to either a second-order point or the tricritical point in the mean-field Blume--Capel model. We show that the thermodynamic magnetization and the finite-size magnetization are asymptotic when the parameter $\alpha$ governing the speed at which the sequence approaches criticality is below a certain threshold $\alpha_0$. However, when $\alpha$ exceeds $\alpha_0$, the thermodynamic magnetization converges to 0 much faster than the finite-size magnetization. The asymptotic behavior of the finite-size magnetization is proved via a moderate deviation principle when $0\alpha_0$. To the best of our knowledge, our results are the first rigorous confirmation of the statistical mechanical theory of finite-size scaling for a mean-field model.Comment: Published in at http://dx.doi.org/10.1214/10-AAP679 the Annals of Applied Probability (http://www.imstat.org/aap/) by the Institute of Mathematical Statistics (http://www.imstat.org

Ginzburg-Landau Polynomials and the Asymptotic Behavior of the Magnetization Near Critical and Tricritical Points

For the mean-field version of an important lattice-spin model due to Blume and Capel, we prove unexpected connections among the asymptotic behavior of the magnetization, the structure of the phase transitions, and a class of polynomials that we call the Ginzburg-Landau polynomials. The model depends on the parameters n, beta, and K, which represent, respectively, the number of spins, the inverse temperature, and the interaction strength. Our main focus is on the asymptotic behavior of the magnetization m(beta_n,K_n) for appropriate sequences (beta_n,K_n) that converge to a second-order point or to the tricritical point of the model and that lie inside various subsets of the phase-coexistence region. The main result states that as (beta_n,K_n) converges to one of these points (beta,K), m(beta_n,K_n) ~ c |beta - beta_n|^gamma --> 0. In this formula gamma is a positive constant, and c is the unique positive, global minimum point of a certain polynomial g that we call the Ginzburg-Landau polynomial. This polynomial arises as a limit of appropriately scaled free-energy functionals, the global minimum points of which define the phase-transition structure of the model. For each sequence (beta_n,K_n) under study, the structure of the global minimum points of the associated Ginzburg-Landau polynomial mirrors the structure of the global minimum points of the free-energy functional in the region through which (beta_n,K_n) passes and thus reflects the phase-transition structure of the model in that region. The properties of the Ginzburg-Landau polynomials make rigorous the predictions of the Ginzburg-Landau phenomenology of critical phenomena, and the asymptotic formula for m(beta_n,K_n) makes rigorous the heuristic scaling theory of the tricritical point.Comment: 70 pages, 8 figure

Pursuing the Strange Stop Interpretation of the HERA Large Q2Q^2 data

We explore the possible interpretation of the large-$Q^2$ anomaly reported by the H1 and ZEUS collaborations in terms of stop squark production off a strange quark in the proton via an R-violating interaction. This "strange stop" interpretation is constrained by LEP measurements of the $Z \to e^+ e^-$ decay rate in addition to constraints from the electroweak $\rho$ parameter and CDF and D0 searches for first-generation leptoquarks. We investigate the interplay between these constraints, taking full account of stop mixing effects. We find that if $m_{\tilde t} \le 200$ GeV only relatively small domains of the chargino and neutralino parameters are consistent with these constraints, and explore the extent to which this scenario may be probed further by searches for contact interactions at LEP~2 and experiments with $e^-$ and polarized beams at HERA

Graph Separation and Search Number

We relate two concepts in graph theory and algorithmic complexity, namely the search number and the vertex separation of a graph. Lengauer has previously related vertex separation to progressive black/white pebble demand. Let a (G) denote the search number and vs(G) denote the vertex separation of a connected, undirected graph G. We show that vs(G) \u3c s(G) \u3c vs(G) +2 and we give a simple transformation from G to G^1 such that vs(G^1) = s(G). We give algorithm that, for any tree T, compute vs(T) in linear time and compute an optimal layout with respect to vertex separation in time O(n log n). We characterize those trees having a given vertex separation and describe the smallest such trees. We give an algorithm which, for all fixed k\u3e1, decides the problem: Is vs(G

CP Violation in the Minimal Supersymmetric Seesaw Model

We study CP violation in the lepton sector of the supersymmetric extension of the Standard Model with three generations of massive singlet neutrinos with Yukawa couplings $Y_\nu$ to lepton doublets, in a minimal seesaw model for light neutrino masses and mixing. This model contains six physical CP-violating parameters, namely the phase $\delta$ observable in oscillations between light neutrino species, two Majorana phases $\phi_{1,2}$ that affect $\beta \beta_{0 \nu}$ decays, and three independent phases appearing in ${Y_\nu}{Y_\nu}^\dagger$, that control the rate of leptogenesis. Renormalization of the soft supersymmetry-breaking parameters induces observable CP violation at low energies, including T-odd asymmetries in polarized $\mu\to eee$ and $\tau \to \ell \ell \ell$ decays, as well as lepton electric dipole moments. In the leading-logarithmic approximation in which the massive singlet neutrinos are treated as degenerate, these low-energy observables are sensitive via ${Y_\nu}^\dagger{Y_\nu}$ to just one combination of the leptogenesis and light-neutrino phases. We present numerical results for the T-odd asymmetry in polarized $\mu\to eee$ decay, which may be accessible to experiment, but the lepton electric dipole moments are very small in this approximation. To the extent that the massive singlet neutrinos are not degenerate, low-energy observables become sensitive also to two other combinations of leptogenesis and light-neutrino phases, in this minimal supersymmetric seesaw model

On the thermal regeneration rate for light gravitinos in the early universe

We investigate the light gravitino regeneration rate in the early Universe in models based on N=1 supergravity. Motivated by a recent claim by Fischler, we evaluate finite-temperature effects on the gravitino regeneration rate due to the hot primordial plasma for a wide range of the supersymmetry-breaking scale F. We find that thermal corrections to the gravitino pole mass and to the Goldstino coupling are negligible for a wide range of temperatures, thereby justifying the extension of the equivalence theorem for the helicity-1/2 gravitino and Goldstino to a hot primordial plasma background. Utilizing the Braaten-Pisarski resummation method, the helicity-1/2 gravitino regeneration rate is found to be 0.25 \alpha_s(T) \log(1/\alpha_s(T))|{m_{\rm soft}/F}|^2 T^3(1 + \alpha_s(T) \log(1/\alpha_s(T)) + T^2 / |F|) up to a calculable, model-dependent {\cal O}(1) numerical factor. We review the implications of this regeneration rate for supergravity cosmology, focusing in particular on scenaria for baryogenesis

The Supersymmetric Parameter Space in Light of B-physics Observables and Electroweak Precision Data

Indirect information about the possible scale of supersymmetry (SUSY) breaking is provided by B-physics observables (BPO) as well as electroweak precision observables (EWPO). We combine the constraints imposed by recent measurements of the BPO BR(b -> s gamma), BR(B_s -> mu^+ mu^-), BR(B_u -> tau nu_tau) and Delta M_{B_s} with those obtained from the experimental measurements of the EWPO M_W, sin^2 theta_eff, Gamma_Z, (g-2)_mu and M_h, incorporating the latest theoretical calculations of these observables within the Standard Model and supersymmetric extensions. We perform a chi^2 fit to the parameters of the constrained minimal supersymmetric extension of the Standard Model (CMSSM), in which the SUSY-breaking parameters are universal at the GUT scale, and the non-universal Higgs model (NUHM), in which this constraint is relaxed for the soft SUSY-breaking contributions to the Higgs masses. Assuming that the lightest supersymmetric particle (LSP) provides the cold dark matter density preferred by WMAP and other cosmological data, we scan over the remaining parameter space. Within the CMSSM, we confirm the preference found previously for a relatively low SUSY-breaking scale, though there is some slight tension between the EWPO and the BPO. In studies of some specific NUHM scenarios compatible with the cold dark matter constraint we investigate M_A-tan_beta planes and find preferred regions that have values of chi^2 somewhat lower than in the CMSSM

Evidence for variable selective pressures at MC1R

It is widely assumed that genes that influence variation in skin and hair pigmentation are under selection. To date,the melanocortin 1 receptor (MC1R) is the only gene identified that explains substantial phenotypic variance inhuman pigmentation. Here we investigate MC1R polymorphism in several populations, for evidence of selection.We conclude that MC1R is under strong functional constraint in Africa, where any diversion from eumelanin production (black pigmentation) appears to be evolutionarily deleterious. Although many of the MC1R amino acid variants observed in non-African populations do affect MC1R function and contribute to high levels of MC1R diversity in Europeans, we found no evidence, in either the magnitude or the patterns of diversity, for its enhancement by selection; rather, our analyses show that levels of MC1R polymorphism simply reflect neutral expectations underrelaxation of strong functional constraint outside Africa

Plxnd1 Expression in Thymocytes Regulates Their Intrathymic Migration While That in Thymic Endothelium Impacts Medullary Topology

An important role for plexinD1 in thymic development is inferred from studies of germline Plxnd1 knockout (KO) mice where mislocalized CD69+ thymocytes as well as ectopic thymic subcapsular medullary structures were observed. Given embryonic lethality of the Plxnd1−/− genotype, fetal liver transplantation was employed in these prior analyses. Such embryonic hematopoietic reconstitution may have transferred Plxnd1 KO endothelial and/or epithelial stem cells in addition to Plxnd1 KO lymphoid progenitors, thereby contributing to that phenotype. Here we use Plxnd1flox/flox mice crossed to pLck-Cre, pKeratin14-Cre, or pTek-Cre transgenic animals to create cell-type specific conditional knockout (CKO) lines involving thymocytes (D1ThyCKO), thymic epithelium (D1EpCKO), and thymic endothelium (D1EnCKO), respectively. These CKOs allowed us to directly assess the role of plexinD1 in each lineage. Loss of plexinD1 expression on double positive (DP) thymocytes leads to their aberrant migration and cortical retention after TCR-mediated positive selection. In contrast, ectopic medulla formation is a consequence of loss of plexinD1 expression on endothelial cells, in turn linked to dysregulation of thymic angiogenesis. D1EpCKO thymi manifest neither abnormality. Collectively, our findings underscore the non-redundant roles for plexinD1 on thymocytes and endothelium, including the dynamic nature of medulla formation resulting from crosstalk between these thymic cellular components

Dispute Resolution, Legal Reasoning and Good Governance: learning lessons from appeals on selection in sport

Research Question: How do legal norms and reasoning processes, in relation to selection appeals, underpin the concepts of good governance and professionalism in sport? Research Methods: This is primarily a theoretical paper that outlines the reasoning techniques and methodology of law as an academic and professional discipline in interpreting, explaining and understanding arbitral decisions related to selection in sport. It draws upon four exemplar cases from the UK dispute resolution body, Sports Resolutions, to illustrate the over-arching norms and principles inherent in legal reasoning and demonstrate how they form part of the normative framework for good governance. Results and Findings: This paper demonstrates how legal reasoning processes, exemplified by dispute resolution cases, provide indicators of good governance in sport. It suggests that a basic understanding of key legal norms and the legal reasoning process would reduce the likelihood of arbitration and appeal against decisions made by SGBs. It concludes that there should be greater dissemination of arbitration decisions by dispute resolution services and that these decisions should be used as education and professional development tools to illustrate the way in which legal norms and reasoning processes are applied. Implications: This paper demonstrates the importance of legal norms and reasoning processes to the concept of good governance in sport. It illustrates how better knowledge and understanding of the way in which arbitral judgements are reached could facilitate improved policy creation and implementation, thereby enhancing good governance, increased professionalism and more robust decision making within SGBs