The critical fugacity for surface adsorption of self-avoiding walks on the honeycomb lattice is 1+21+\sqrt{2}

In 2010, Duminil-Copin and Smirnov proved a long-standing conjecture of Nienhuis, made in 1982, that the growth constant of self-avoiding walks on the hexagonal (a.k.a. honeycomb) lattice is $\mu=\sqrt{2+\sqrt{2}}.$ A key identity used in that proof was later generalised by Smirnov so as to apply to a general O(n) loop model with $n\in [-2,2]$ (the case $n=0$ corresponding to SAWs). We modify this model by restricting to a half-plane and introducing a surface fugacity $y$ associated with boundary sites (also called surface sites), and obtain a generalisation of Smirnov's identity. The critical value of the surface fugacity was conjectured by Batchelor and Yung in 1995 to be $y_{\rm c}=1+2/\sqrt{2-n}.$ This value plays a crucial role in our generalized identity, just as the value of growth constant did in Smirnov's identity. For the case $n=0$, corresponding to \saws\ interacting with a surface, we prove the conjectured value of the critical surface fugacity. A crucial part of the proof involves demonstrating that the generating function of self-avoiding bridges of height $T$, taken at its critical point $1/\mu$, tends to 0 as $T$ increases, as predicted from SLE theory.Comment: Major revision, references updated, 25 pages, 13 figure

Reaction Diffusion Models in One Dimension with Disorder

We study a large class of 1D reaction diffusion models with quenched disorder using a real space renormalization group method (RSRG) which yields exact results at large time. Particles (e.g. of several species) undergo diffusion with random local bias (Sinai model) and react upon meeting. We obtain the large time decay of the density of each specie, their associated universal amplitudes, and the spatial distribution of particles. We also derive the spectrum of exponents which characterize the convergence towards the asymptotic states. For reactions with several asymptotic states, we analyze the dynamical phase diagram and obtain the critical exponents at the transitions. We also study persistence properties for single particles and for patterns. We compute the decay exponents for the probability of no crossing of a given point by, respectively, the single particle trajectories ($\theta$) or the thermally averaged packets ($\bar{\theta}$). The generalized persistence exponents associated to n crossings are also obtained. Specifying to the process $A+A \to \emptyset$ or A with probabilities $(r,1-r)$, we compute exactly the exponents $\delta(r)$ and $\psi(r)$ characterizing the survival up to time t of a domain without any merging or with mergings respectively, and $\delta_A(r)$ and $\psi_A(r)$ characterizing the survival up to time t of a particle A without any coalescence or with coalescences respectively. $\bar{\theta}, \psi, \delta$ obey hypergeometric equations and are numerically surprisingly close to pure system exponents (though associated to a completely different diffusion length). Additional disorder in the reaction rates, as well as some open questions, are also discussed.Comment: 54 pages, Late

Widths of the Hall Conductance Plateaus

We study the charge transport of the noninteracting electron gas in a two-dimensional quantum Hall system with Anderson-type impurities at zero temperature. We prove that there exist localized states of the bulk order in the disordered-broadened Landau bands whose energies are smaller than a certain value determined by the strength of the uniform magnetic field. We also prove that, when the Fermi level lies in the localization regime, the Hall conductance is quantized to the desired integer and shows the plateau of the bulk order for varying the filling factor of the electrons rather than the Fermi level.Comment: 94 pages, v2: a revision of Sec. 5; v3: an error in Sec. 7 is corrected, major revisions of Sec. 7 and Appendix E, Sec. 7 is enlarged to Secs. 7-12, minor corrections; v4: major revisions, accepted for publication in Journal of Statistical Physics; v5: minor corrections, accepted versio

Random walks and polymers in the presence of quenched disorder

After a general introduction to the field, we describe some recent results concerning disorder effects on both `random walk models', where the random walk is a dynamical process generated by local transition rules, and on `polymer models', where each random walk trajectory representing the configuration of a polymer chain is associated to a global Boltzmann weight. For random walk models, we explain, on the specific examples of the Sinai model and of the trap model, how disorder induces anomalous diffusion, aging behaviours and Golosov localization, and how these properties can be understood via a strong disorder renormalization approach. For polymer models, we discuss the critical properties of various delocalization transitions involving random polymers. We first summarize some recent progresses in the general theory of random critical points : thermodynamic observables are not self-averaging at criticality whenever disorder is relevant, and this lack of self-averaging is directly related to the probability distribution of pseudo-critical temperatures $T_c(i,L)$ over the ensemble of samples $(i)$ of size $L$. We describe the results of this analysis for the bidimensional wetting and for the Poland-Scheraga model of DNA denaturation.Comment: 17 pages, Conference Proceedings "Mathematics and Physics", I.H.E.S., France, November 200

Study of ttbar Production in ppbar Collisions Using Total Transverse Energy

We analyze a sample of W + jet events collected with the Collider Detector at Fermilab (CDF) in ppbar collisions at sqrt(s) = 1.8 TeV to study ttbar production. We employ a simple kinematical variable "H", defined as the scalar sum of the transverse energies of the lepton, neutrino and jets. For events with a W boson and four or more jets, the shape of the "H" distribution deviates by 3.8 standard deviations from that expected from known backgrounds to ttbar production. However this distribution agrees well with a linear combination of background and ttbar events, the agreement being best for a top mass of 180 GeV/c^2.Comment: Postscript file (gzip+uuencode). 5-page, two-column PRL format (RevTex). Submitted to Phys. Rev. Lett. 09 June 199

Mixed-methods study in England and Northern Ireland to understand young men who have sex with men’s knowledge and attitudes towards human papillomavirus vaccination

Objectives: Men-who-have-sex-with-men (MSM) are at greater risk for HPV-associated cancers. Since 2016, MSM have been offered the HPV vaccination, which is most effective when received prior to sexual debut, at Genitourinary Medicine clinics in the United Kingdom. In September 2019, the national HPV vaccination programme will be extended to boys. This study aimed to understand young MSM’s (YMSM) knowledge and attitudes towards human papillomavirus (HPV) vaccination. Design: Questionnaires assessed YMSM demographics, sexual behaviour, culture, knowledge and attitudes towards HPV vaccination, and stage of vaccine decision-making using the Precaution Adoption Process Model. Focus groups explored sexual health information sources, attitudes, barriers and facilitators to vaccination, and strategies to support vaccination uptake. Questionnaire data were analysed using descriptive statistics and focus group data were analysed thematically. Setting: Questionnaires were also completed online. Focus groups were conducted within Lesbian Gay Bisexual Trans Queer (LGBTQ) organisational settings and a university student’s union in England and Northern Ireland. Participants: Seventeen YMSM (M=20.5 years) participated in four focus groups and 51 (M=21.1 years) completed questionnaires. Results: Over half of YMSM were aware of HPV (54.9%), yet few (21.6%) had previously discussed vaccination with a Healthcare Professional (HCP). Thematic analyses found YMSM were willing to receive the HPV vaccine. Vaccination programmes requiring YMSM to request the vaccine, particularly prior to sexual orientation disclosure to family and friends, were viewed as unfeasible. Educational campaigns explaining vaccine benefits were indicated as a way to encourage uptake. Conclusions: This study suggests that to effectively implement HPV vaccination for YMSM, this population requires clearer information and greater discussion with their HCP. In support of the decision made by the JCVI, universal vaccination is the most feasible and equitable option. However, the absence of a catch-up programme will leave a significant number of YMSM at risk of HPV infection