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 $4/3$ 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 $\gamma= 1/3$ 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 $Z^3$. On a 3d Euclidean lattice it has equivalent representation in terms of transfer matrix $K(Q_{i},Q_{f})$, which describes the propagation of loops $Q$. We study the spectrum of the transfer matrix $K(Q_{i},Q_{f})$ 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 $\beta_S$ for the space-like plaquettes and $\beta_T$ for the transverse-like plaquettes are different. In the two limits $\beta_S=0$ and $\beta_T=0$ 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 $\beta_T = \beta_S \approx 0.25,$ 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 $\beta_S =0$ 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 $\beta_S =\beta_T$ 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