Numerical estimate of finite size corrections to the free energy of the SK model using Guerra--Toninelli interpolation

I use an interpolating formula introduced by Guerra and Toninelli to investigate numerically the finite size corrections to the free energy of the Sherrington--Kirkpatrick model. The results are compatible with a $(1/12 N) \ln(N/N_0)$ behavior at $T_c$, as predicted by Parisi, Ritort and Slanina, and a $1/N^{2/3}$ behavior below $T_c$

Narrow-band noise due to the moving vortex lattice in superconducting niobium

We report measurements of voltage noise due to vortex motion in Niobium, a conventional low-Tc superconductor. A coherent oscillation leading to narrow band noise (NBN) is evidenced. Its characteristic frequency is a linear function of the overcritical transport current in the flux-flow regime, and hence scales as the main velocity of the vortex flow. The associated length scale is not the intervortex distance but the width of the sample, indicating temporal coherence at a large scale. NBN is also observed in the non linear part of the V(I) at the onset of depinning, in apparent disagreement with a stochastic creep motion of flux bundles. NBN exists in the peak effect region, showing that long range temporal correlations are preserved in this regime.Comment: accepted for publication in Phys Rev

An analyst's take on the BPHZ theorem

We provide a self-contained formulation of the BPHZ theorem in the Euclidean context, which yields a systematic procedure to "renormalise" otherwise divergent integrals appearing in generalised convolutions of functions with a singularity of prescribed order at their origin. We hope that the formulation given in this article will appeal to an analytically minded audience and that it will help to clarify to what extent such renormalisations are arbitrary (or not). In particular, we do not assume any background whatsoever in quantum field theory and we stay away from any discussion of the physical context in which such problems typically arise.Comment: Accepted versio

Cosmic microwave background multipole alignments in slab topologies

Several analyses of the microwave sky maps from the Wilkinson Microwave Anisotropy Probe (WMAP) have drawn attention to alignments amongst the low-order multipoles. Amongst the various possible explanations, an effect of cosmic topology has been invoked by several authors. We focus on an alignment of the first four multipoles (\ell = 2 to 5) found by Land and Magueijo (2005), and investigate the distribution of their alignment statistic for a set of simulated cosmic microwave background maps for cosmologies with slab-like topology. We find that this topology does offer a modest increase in the probability of the observed value, but that even for the smallest topology considered the probability of the observed value remains below one percent.Comment: 6 pages RevTex with 6 figures included. Minor changes to match version accepted as Physical Review D Rapid Communicatio