Exact conjectured expressions for correlations in the dense O(1)(1) loop model on cylinders

We present conjectured exact expressions for two types of correlations in the dense O$(n=1)$ loop model on $L\times \infty$ square lattices with periodic boundary conditions. These are the probability that a point is surrounded by $m$ loops and the probability that $k$ consecutive points on a row are on the same or on different loops. The dense O$(n=1)$ loop model is equivalent to the bond percolation model at the critical point. The former probability can be interpreted in terms of the bond percolation problem as giving the probability that a vertex is on a cluster that is surrounded by \floor{m/2} clusters and \floor{(m+1)/2} dual clusters. The conjectured expression for this probability involves a binomial determinant that is known to give weighted enumerations of cyclically symmetric plane partitions and also of certain types of families of nonintersecting lattice paths. By applying Coulomb gas methods to the dense O$(n=1)$ loop model, we obtain new conjectures for the asymptotics of this binomial determinant.Comment: 17 pages, replaced by version accepted by JSTA

Hydrogen diffusion and microstructure in undoped and boron-doped hydrogenated amorphous silicon: an IR and SIMS study

Hydrogenated amorphous silicon (a-Si:H) prepared by rf sputtering of a polycrystalline Si target at various rf powers 50 ≤ P ≤ 550 W (0.27-2.97 W/cm[superscript]2), target to substrate distance 1 ≤ d ≤ 2[superscript]\u27\u27, and varying hydrogen partial pressures. Doping was accomplished by introducing diborane (B[subscript]2H[subscript]6) in the plasma. Hydrogen diffusion was studied from the depth profiles obtained from the SIMS on multilayered a-Si:H/a-Si:(H,D)/a-Si:H samples;The properties of the samples were characterized by IR absorption, optical gap measurements and ESR. IR yielded quantitative and qualitative information total hydrogen content and the nature of hydrogen bonding, respectively. Hence the hydrogen microstructure of the samples could be varied in a systematic manner and monitored from the hydrogen vibrational modes. The ESR gave information on the number of paramagnetic defects per unit volume in the samples;The IR absorption of both as-deposited and annealed samples were closely monitored and the results clearly demonstrate a strong correlation between hydrogen diffusion and its microstructure. It is shown that microvoids in a-Si:H play a critical role in the process of diffusion by inducing deep hydrogen trapping sites that render them immobile. Consequently, as the microvoid density increases beyond a critical density (corresponding to N[subscript] d ≥ 6.5 at. %) hydrogen diffusion is totally quenched. The diffusion results are discussed both in the context of multiple trapping transport of hydrogen in an exponential distribution of trapping sites and the floating bond model;As expected the hydrogen diffusion in boron-doped a-Si:H is faster than undoped material by a few orders of magnitude. The diffusion results have shown a significant departure from the power-law time dependence upon prolonged annealing. Such a departure has not been reported before. It is suspected that this deviation is caused by structural relaxations of the silicon network. ftn*DOE Report IS-T-1506. This work was performed under contract No W-7405-Eng-82 with US Department of Energy

Has DAMA Detected Self-Interacting Dark Matter?

We consider a model in which dark matter consists of a large self-interacting component (SIDM particles) and a small component with strong interactions with baryons (SIMPs). We show that the DAMA annual modulation signal can be caused by SIDM particles interacting with SIMPs trapped in iodine nuclei in the DAMA/NaI detector.Comment: 4 pages, version accepted by PR

The XXZ spin chain at Δ=−1/2\Delta=- {1/2}: Bethe roots, symmetric functions and determinants

A number of conjectures have been given recently concerning the connection between the antiferromagnetic XXZ spin chain at $\Delta = - \frac12$ and various symmetry classes of alternating sign matrices. Here we use the integrability of the XXZ chain to gain further insight into these developments. In doing so we obtain a number of new results using Baxter's $Q$ function for the XXZ chain for periodic, twisted and open boundary conditions. These include expressions for the elementary symmetric functions evaluated at the groundstate solution of the Bethe roots. In this approach Schur functions play a central role and enable us to derive determinant expressions which appear in certain natural double products over the Bethe roots. When evaluated these give rise to the numbers counting different symmetry classes of alternating sign matrices.Comment: 11 pages, revte

Exact asymptotics of the characteristic polynomial of the symmetric Pascal matrix

We have obtained the exact asymptotics of the determinant $\det_{1\leq r,s\leq L}[\binom{r+s-2}{r-1}+\exp(i\theta)\delta_{r,s}]$. Inverse symbolic computing methods were used to obtain exact analytical expressions for all terms up to relative order $L^{-14}$ to the leading term. This determinant is known to give weighted enumerations of cyclically symmetric plane partitions, weighted enumerations of certain families of vicious walkers and it has been conjectured to be proportional to the one point function of the O$(1)$ loop model on a cylinder of circumference $L$. We apply our result to the loop model and give exact expressions for the asymptotics of the average of the number of loops surrounding a point and the fluctuation in this number. For the related bond percolation model, we give exact expressions for the asymptotics of the probability that a point is on a cluster that wraps around a cylinder of even circumference and the probability that a point is on a cluster spanning a cylinder of odd circumference.Comment: Version accepted by JCTA. Introduction rewritte

Expansions about Free-Fermion Models

A simple technique for expanding the free energy of general six-vertex models about free-fermion points is introduced. This technique is used to verify a Coulomb gas prediction about the behavior of the leading singularity in the free energy of the staggered F-model at zero staggered field.Comment: 8 page