Quark-Antiquark Energy Density Function applied to Di-Gauge Boson Production at the LHC

In view of the start up of the 14 TeV pp Large Hadron Collider the quark anti-quark reactions leading to the final states W^+W^-, W^+-Z^0 and Z^0Z^0 are studied, in the frame workn of the Standard Model (SM), using helicity amplitudes. The differential and total cross sections are first evaluated in the parton-parton center of mass system. They are then transformed to their expected behavior in pp collisions through the parton-parton Energy Density Functions which are here derived from the known Parton Density Functions of the proton. In particular the single and joint longitudinal polarizations of the final state di-bosons are calculated. The effect on these reactions from the presence of s-channel heavy vector bosons, like the W' and Z', are evaluated to explore the possibility to utilize the gauge boson pair production as a probe for these 'Beyond the SM' phenomena.Comment: 15 pages and 8 figures

Non-Local Finite-Size Effects in the Dimer Model

We study the finite-size corrections of the dimer model on ∞ × N square lattice with two different boundary conditions: free and periodic. We find that the finite-size corrections depend in a crucial way on the parity of N, and show that, because of certain non-local features present in the model, a change of parity of N induces a change of boundary condition. Taking a careful account of this, these unusual finite-size behaviours can be fully explained in the framework of the c = -2 logarithmic conformal field theory

Introduction to the Sandpile Model

This article is based on a talk given by one of us (EVI) at the conference ``StatPhys-Taipei-1997''. It overviews the exact results in the theory of the sandpile model and discusses shortly yet unsolved problem of calculation of avalanche distribution exponents. The key ingredients include the analogy with the critical reaction-diffusion system, the spanning tree representation of height configurations and the decomposition of the avalanche process into waves of topplings

The totally asymmetric exclusion process on a ring: Exact relaxation dynamics and associated model of clustering transition

The totally asymmetric simple exclusion process in discrete time is considered on finite rings with fixed number of particles. A translation-invariant version of the backward-ordered sequential update is defined for periodic boundary conditions. We prove that the so defined update leads to a stationary state in which all possible particle configurations have equal probabilities. Using the exact analytical expression for the propagator, we find the generating function for the conditional probabilities, average velocity and diffusion constant at all stages of evolution. An exact and explicit expression for the stationary velocity of TASEP on rings of arbitrary size and particle filling is derived. The evolution of small systems towards a steady state is clearly demonstrated. Considering the generating function as a partition function of a thermodynamic system, we study its zeros in planes of complex fugacities. At long enough times, the patterns of zeroes for rings with increasing size provide evidence for a transition of the associated two-dimensional lattice paths model into a clustered phase at low fugacities.Comment: 9 pages 5 figures accepted for publication in Physica

Generalized Green Functions and current correlations in the TASEP

We study correlation functions of the totally asymmetric simple exclusion process (TASEP) in discrete time with backward sequential update. We prove a determinantal formula for the generalized Green function which describes transitions between positions of particles at different individual time moments. In particular, the generalized Green function defines a probability measure at staircase lines on the space-time plane. The marginals of this measure are the TASEP correlation functions in the space-time region not covered by the standard Green function approach. As an example, we calculate the current correlation function that is the joint probability distribution of times taken by selected particles to travel given distance. An asymptotic analysis shows that current fluctuations converge to the ${Airy}_2$ process.Comment: 46 pages, 3 figure

From elongated spanning trees to vicious random walks

Given a spanning forest on a large square lattice, we consider by combinatorial methods a correlation function of $k$ paths ($k$ is odd) along branches of trees or, equivalently, $k$ loop--erased random walks. Starting and ending points of the paths are grouped in a fashion a $k$--leg watermelon. For large distance $r$ between groups of starting and ending points, the ratio of the number of watermelon configurations to the total number of spanning trees behaves as $r^{-\nu} \log r$ with $\nu = (k^2-1)/2$. Considering the spanning forest stretched along the meridian of this watermelon, we see that the two--dimensional $k$--leg loop--erased watermelon exponent $\nu$ is converting into the scaling exponent for the reunion probability (at a given point) of $k$ (1+1)--dimensional vicious walkers, $\tilde{\nu} = k^2/2$. Also, we express the conjectures about the possible relation to integrable systems.Comment: 27 pages, 6 figure

Infinite volume limit of the Abelian sandpile model in dimensions d >= 3

We study the Abelian sandpile model on Z^d. In dimensions at least 3 we prove existence of the infinite volume addition operator, almost surely with respect to the infinite volume limit mu of the uniform measures on recurrent configurations. We prove the existence of a Markov process with stationary measure mu, and study ergodic properties of this process. The main techniques we use are a connection between the statistics of waves and uniform two-component spanning trees and results on the uniform spanning tree measure on Z^d.Comment: First version: LaTeX; 29 pages. Revised version: LaTeX; 29 pages. The main result of the paper has been extended to all dimensions at least 3, with a new and simplyfied proof of finiteness of the two-component spanning tree. Second revision: LaTeX; 32 page

Dynamically Driven Renormalization Group Applied to Sandpile Models

The general framework for the renormalization group analysis of self-organized critical sandpile models is formulated. The usual real space renormalization scheme for lattice models when applied to nonequilibrium dynamical models must be supplemented by feedback relations coming from the stationarity conditions. On the basis of these ideas the Dynamically Driven Renormalization Group is applied to describe the boundary and bulk critical behavior of sandpile models. A detailed description of the branching nature of sandpile avalanches is given in terms of the generating functions of the underlying branching process.Comment: 18 RevTeX pages, 5 figure

Dissipative Abelian Sandpiles and Random Walks

We show that the dissipative Abelian sandpile on a graph L can be related to a random walk on a graph which consists of L extended with a trapping site. From this relation it can be shown, using exact results and a scaling assumption, that the dissipative sandpiles' correlation length exponent \nu always equals 1/d_w, where d_w is the fractal dimension of the random walker. This leads to a new understanding of the known results that \nu=1/2 on any Euclidean lattice. Our result is however more general and as an example we also present exact data for finite Sierpinski gaskets which fully confirm our predictions.Comment: 10 pages, 1 figur

Renormalization group approach to an Abelian sandpile model on planar lattices

One important step in the renormalization group (RG) approach to a lattice sandpile model is the exact enumeration of all possible toppling processes of sandpile dynamics inside a cell for RG transformations. Here we propose a computer algorithm to carry out such exact enumeration for cells of planar lattices in RG approach to Bak-Tang-Wiesenfeld sandpile model [Phys. Rev. Lett. {\bf 59}, 381 (1987)] and consider both the reduced-high RG equations proposed by Pietronero, Vespignani, and Zapperi (PVZ) [Phys. Rev. Lett. {\bf 72}, 1690 (1994)] and the real-height RG equations proposed by Ivashkevich [Phys. Rev. Lett. {\bf 76}, 3368 (1996)]. Using this algorithm we are able to carry out RG transformations more quickly with large cell size, e.g. $3 \times 3$ cell for the square (sq) lattice in PVZ RG equations, which is the largest cell size at the present, and find some mistakes in a previous paper [Phys. Rev. E {\bf 51}, 1711 (1995)]. For sq and plane triangular (pt) lattices, we obtain the only attractive fixed point for each lattice and calculate the avalanche exponent $\tau$ and the dynamical exponent $z$. Our results suggest that the increase of the cell size in the PVZ RG transformation does not lead to more accurate results. The implication of such result is discussed.Comment: 29 pages, 6 figure