Physics – Condensed Matter – Statistical Mechanics
Scientific paper
2008-06-07
Phys. Rev. E vol 78 041126 (2008)
Physics
Condensed Matter
Statistical Mechanics
14 pages, 9 figures
Scientific paper
10.1103/PhysRevE.78.041126
To each directed acyclic graph (this includes some D-dimensional lattices) one can associate some abelian algebras that we call directed abelian algebras (DAA). On each site of the graph one attaches a generator of the algebra. These algebras depend on several parameters and are semisimple. Using any DAA one can define a family of Hamiltonians which give the continuous time evolution of a stochastic process. The calculation of the spectra and ground state wavefunctions (stationary states probability distributions) is an easy algebraic exercise. If one considers D-dimensional lattices and choose Hamiltonians linear in the generators, in the finite-size scaling the Hamiltonian spectrum is gapless with a critical dynamic exponent $z = D$. One possible application of the DAA is to sandpile models. In the paper we present this application considering one and two dimensional lattices. In the one dimensional case, when the DAA conserves the number of particles, the avalanches belong to the random walker universality class (critical exponent $\sigma_{\tau} = 3/2$). We study the local densityof particles inside large avalanches showing a depletion of particles at the source of the avalanche and an enrichment at its end. In two dimensions we did extensive Monte-Carlo simulations and found $\sigma_{\tau} = 1.782 \pm 0.005$.
Alcaraz Francisco Castilho
Rittenberg Vladimir
No associations
LandOfFree
Directed abelian algebras and their applications to stochastic models does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.
If you have personal experience with Directed abelian algebras and their applications to stochastic models, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Directed abelian algebras and their applications to stochastic models will most certainly appreciate the feedback.
Profile ID: LFWR-SCP-O-65490