Logarithmic two-point correlators in the Abelian sandpile model

We present the detailed calculations of the asymptotics of two-site correlation functions for height variables in the two-dimensional Abelian sandpile model. By using combinatorial methods for the enumeration of spanning trees, we extend the well-known result for the correlation $\sigma_{1,1} \simeq 1/r^4$ of minimal heights $h_1=h_2=1$ to $\sigma_{1,h} = P_{1,h}-P_1P_h$ for height values $h=2,3,4$. These results confirm the dominant logarithmic behaviour $\sigma_{1,h} \simeq (c_h\log r + d_h)/r^4 + {\cal O}(r^{-5})$ for large $r$, predicted by logarithmic conformal field theory based on field identifications obtained previously. We obtain, from our lattice calculations, the explicit values for the coefficients $c_h$ and $d_h$ (the latter are new).Comment: 28 page

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

Three-leg correlations in the two component spanning tree on the upper half-plane

We present a detailed asymptotic analysis of correlation functions for the two component spanning tree on the two-dimensional lattice when one component contains three paths connecting vicinities of two fixed lattice sites at large distance $s$ apart. We extend the known result for correlations on the plane to the case of the upper half-plane with closed and open boundary conditions. We found asymptotics of correlations for distance $r$ from the boundary to one of the fixed lattice sites for the cases $r\gg s \gg 1$ and $s \gg r \gg 1$.Comment: 16 pages, 5 figure

Abelian Sandpile Model on the Honeycomb Lattice

We check the universality properties of the two-dimensional Abelian sandpile model by computing some of its properties on the honeycomb lattice. Exact expressions for unit height correlation functions in presence of boundaries and for different boundary conditions are derived. Also, we study the statistics of the boundaries of avalanche waves by using the theory of SLE and suggest that these curves are conformally invariant and described by SLE2.Comment: 24 pages, 5 figure

Two-dimensional spanning webs as (1,2) logarithmic minimal model

A lattice model of critical spanning webs is considered for the finite cylinder geometry. Due to the presence of cycles, the model is a generalization of the known spanning tree model which belongs to the class of logarithmic theories with central charge $c=-2$. We show that in the scaling limit the universal part of the partition function for closed boundary conditions at both edges of the cylinder coincides with the character of symplectic fermions with periodic boundary conditions and for open boundary at one edge and closed at the other coincides with the character of symplectic fermions with antiperiodic boundary conditions.Comment: 21 pages, 3 figure

Specific heat and heat conductivity of the BaTiO3 polycrystalline films with the thickness in the range 20 - 1100 nm

Thermal properties - specific heat and heat conductivity coefficient - of polycrystalline BaTiO3 films on massive substrates were studied as a function of the temperature and the film thickness by ac-hot probe method. The anomalies of specific heat with decreasing of the film thickness from 1100 to 20 nm revealed the reducing of critical temperature (Tc) and excess entropy of the ferroelectric phase transition, which becomes diffused. The critical thickness of the film at which Tc = 0 estimated as 2.5 nm.Comment: 12 pages, 7 figures, 2 tables, 450kb; submitted to J.Phys.:Cond.Mat

Usage of GIS technologies for ecosystems monitoring

Aiming to obtain an estimate of the changes in the position of the upper boundary of open spruce forests in the Zigal’ga mountain ridge (South Urals), we used a set of methods: a comparison of aerial photographs, satellite images, and repeated landscape photographs made at different times. A qualitative and quantitative assessment of these changes for the period from 1958 to 2012 was made. The results of the study show that tree vegetation has been actively expanding to higher elevations over the past 54 years. Altitudinal shift of upper boundaries of open forests along the median was 0.74 m/year, and horizontal shift was 0.20 m/year. Expanding open forests are explained by climate warming and increasing humidity, especially in the cold period of the year in the South Urals. © 2018 CEUR-WS. All rights reserved.This work was supported by RFBR grant 16-05-00454

The development remission of acromegaly in the outcome of intraoperative bleeding in somatoprolactinomas

In this article we describe a rare case of spontaneous remission of acromegaly as a consequence of hemorrhage to pituitary adenoma and subarachnoid space, followed after intraoperative bleeding during transnasal removal of somatoprolactinomas