10,771 research outputs found
A Complete Classification of Tractability in RCC-5
We investigate the computational properties of the spatial algebra RCC-5
which is a restricted version of the RCC framework for spatial reasoning. The
satisfiability problem for RCC-5 is known to be NP-complete but not much is
known about its approximately four billion subclasses. We provide a complete
classification of satisfiability for all these subclasses into polynomial and
NP-complete respectively. In the process, we identify all maximal tractable
subalgebras which are four in total.Comment: See http://www.jair.org/ for an online appendix and other files
accompanying this articl
Avalanche size distribution in a random walk model
We introduce a simple model for the size distribution of avalanches based on
the idea that the front of an avalanche can be described by a directed random
walk. The model captures some of the qualitative features of earthquakes,
avalanches and other self-organized critical phenomena in one dimension. We
find scaling laws relating the frequency, size and width of avalanches and an
exponent in the size distribution law.Comment: 16 pages Latex, macros included, 3 postscript figure
The phase diagram of an Ising model on a polymerized random surface
We construct a random surface model with a string susceptibility exponent one
quarter by taking an Ising model on a random surface and introducing an
additional degree of freedom which amounts to allowing certain outgrowths on
the surfaces. Fine tuning the Ising temperature and the weight factor for
outgrowths we find a triple point where the susceptibility exponent is one
quarter. At this point magnetized and nonmagnetized gravity phases meet a
branched polymer phase.Comment: Latex file, 10 pages, macros included. Two EPS figure
A Solvable 2D Quantum Gravity Model with \GAMMA >0
We consider a model of discretized 2d gravity interacting with Ising spins
where phase boundaries are restricted to have minimal length and show
analytically that the critical exponent at the spin transition
point. The model captures the numerically observed behavior of standard
multiple Ising spins coupled to 2d gravity.Comment: Latex, 9 pages, NBI-HE-94-0
The Spectrum of the Loop Transfer Matrix on Finite Lattice
We consider the model of random surfaces with extrinsic curvature term
embedded into 3d Euclidean lattice . On a 3d Euclidean lattice it has
equivalent representation in terms of transfer matrix , which
describes the propagation of loops . We study the spectrum of the transfer
matrix on finite dimensional lattices. The renormalisation
group technique is used to investigate phase structure of the model and its
critical behaviour.Comment: 10 pages, 5 figures, Latex, psfi
Three-dimensional gonihedric spin system
We perform Monte Carlo simulations of a three-dimensional spin system with a
Hamiltonian which contains only four-spin interaction term. This system
describes random surfaces with extrinsic curvature - gonihedric action. We
study the anisotropic model when the coupling constants for the
space-like plaquettes and for the transverse-like plaquettes are
different. In the two limits and the system has been
solved exactly and the main interest is to see what happens when we move away
from these points towards the isotropic point, where we recover the original
model. We find that the phase transition is of first order for while away from this point it becomes weaker and
eventually turns to a crossover. The conclusion which can be drown from this
result is that the exact solution at the point in terms of
2d-Ising model should be considered as a good zero order approximation in the
description of the system also at the isotropic point and
clearly confirms the earlier findings that at the isotropic point the original
model shows a first order phase transition.Comment: 11 pages, 10 figures, shortened versio
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