100 research outputs found
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
Loop transfer matrix and gonihedric loop diffusion
We study a class of statistical systems which simulate 3D gonihedric system
on euclidean lattice. We have found the exact partition function of the
3D-model and the corresponding critical indices analysing the transfer matrix
which describes the propagation of loops on a lattice. The
connection between 3D gonihedric system and 2D-Ising model is clearly seen.Comment: 14 pages, Late
The spectral dimension of generic trees
We define generic ensembles of infinite trees. These are limits as
of ensembles of finite trees of fixed size , defined in terms
of a set of branching weights. Among these ensembles are those supported on
trees with vertices of a uniformly bounded order. The associated probability
measures are supported on trees with a single spine and Hausdorff dimension
. Our main result is that their spectral dimension is , and
that the critical exponent of the mass, defined as the exponential decay rate
of the two-point function along the spine, is 1/3
Condensation in nongeneric trees
We study nongeneric planar trees and prove the existence of a Gibbs measure
on infinite trees obtained as a weak limit of the finite volume measures. It is
shown that in the infinite volume limit there arises exactly one vertex of
infinite degree and the rest of the tree is distributed like a subcritical
Galton-Watson tree with mean offspring probability . We calculate the rate
of divergence of the degree of the highest order vertex of finite trees in the
thermodynamic limit and show it goes like where is the size of the
tree. These trees have infinite spectral dimension with probability one but the
spectral dimension calculated from the ensemble average of the generating
function for return probabilities is given by if the weight
of a vertex of degree is asymptotic to .Comment: 57 pages, 14 figures. Minor change
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