163 research outputs found
Statistical mechanical systems on complete graphs, infinite exchangeability, finite extensions and a discrete finite moment problem
We show that a large collection of statistical mechanical systems with
quadratically represented Hamiltonians on the complete graph can be extended to
infinite exchangeable processes. This extends a known result for the
ferromagnetic Curie--Weiss Ising model and includes as well all ferromagnetic
Curie--Weiss Potts and Curie--Weiss Heisenberg models. By de Finetti's theorem,
this is equivalent to showing that these probability measures can be expressed
as averages of product measures. We provide examples showing that
``ferromagnetism'' is not however in itself sufficient and also study in some
detail the Curie--Weiss Ising model with an additional 3-body interaction.
Finally, we study the question of how much the antiferromagnetic Curie--Weiss
Ising model can be extended. In this direction, we obtain sharp asymptotic
results via a solution to a new moment problem. We also obtain a ``formula''
for the extension which is valid in many cases.Comment: Published at http://dx.doi.org/10.1214/009117906000001033 in the
Annals of Probability (http://www.imstat.org/aop/) by the Institute of
Mathematical Statistics (http://www.imstat.org
Coupling Surfaces and Weak Bernoulli in One and Higher Dimensions
AbstractWe propose a notion of weak Bernoulli in all dimensions which generalizes the usual definition in dimension 1. The key idea is the concept of acoupling surface. We relate this notion to previously studied properties and discuss a number of possible variants in dimension 1. We also show that the Ising model, at low temperature, is weak Bernoulli with an explicit description of the coupling surface
Supergeometry of Three Dimensional Black Holes
We show how the supersymmetric properties of three dimensional black holes
can be obtained algebraically. The black hole solutions are constructed as
quotients of the supergroup by a discrete subgroup of its
isometry supergroup. The generators of the action of the isometry supergroup
which commute with these identifications are found. These yield the
supersymmetries for the black hole as found in recent studies as well as the
usual geometric isometries. It is also shown that in the limit of vanishing
cosmological constant, the black hole vacuum becomes a null orbifold, a
solution previously discussed in the context of string theory.Comment: 12 pages, harvmac, discussion of rotating black hole added, some
minor corrections, reference adde
Time-Symmetric Initial Data for Multi-Body Solutions in Three Dimensions
Time-symmetric initial data for two-body solutions in three dimensional
anti-deSitter gravity are found. The spatial geometry has constant negative
curvature and is constructed as a quotient of two-dimensional hyperbolic space.
Apparent horizons correspond to closed geodesics. In an open universe, it is
shown that two black holes cannot exist separately, but are necessarily
enclosed by a third horizon. In a closed universe, two separate black holes can
exist provided there is an additional image mass.Comment: 12 pages, harvmac macro, minor changes in wordin
Lattice Universes in 2+1-dimensional gravity
Lattice universes are spatially closed space-times of spherical topology in
the large, containing masses or black holes arranged in the symmetry of a
regular polygon or polytope. Exact solutions for such spacetimes are found in
2+1 dimensions for Einstein gravity with a non-positive cosmological constant.
By means of a mapping that preserves the essential nature of geodesics we
establish analogies between the flat and the negative curvature cases. This map
also allows treatment of point particles and black holes on a similar footing.Comment: 14 pages 7 figures, to appear in Festschrift for Vince Moncrief (CQG
Back-reaction of a conformal field on a three-dimensional black hole
The first order corrections to the geometry of the (2+1)-dimensional black
hole due to back-reaction of a massless conformal scalar field are computed.
The renormalized stress energy tensor used as the source of Einstein equations
is computed with the Green function for the black-hole background with
transparent boundary conditions. This tensor has the same functional form as
the one found in the nonperturbative case which can be exactly solved. Thus, a
static, circularly symmetric and asymptotically anti-de Sitter black hole
solution of the semiclassical equations is found. The corrections to the
thermodynamic quantities are also computed.Comment: 12 pages, RevTeX, no figure
Exact Results for the BTZ Black Hole
In this review, we summarize exact results for the three-dimensional BTZ
black hole. We use rigorous mathematical results to clarify the general
structure and properties of this black hole spacetime and its microscopic
description. In particular, we study the formation of the black hole by point
particle collisions, leading to an exact analytic determination of the Choptuik
scaling parameter. We also show that a `No Hair Theorem' follows immediately
from a mathematical theorem of hyperbolic geometry, due to Sullivan. A
microscopic understanding of the Bekenstein-Hawking entropy, and decay rate for
massless scalars, is shown to follow from standard results of conformal field
theory.Comment: 24 pages, Latex, Review article to appear in Int. J. Mod. Phys. D, v2
additional reference
Gott Time Machines, BTZ Black Hole Formation, and Choptuik Scaling
We study the formation of BTZ black holes by the collision of point
particles. It is shown that the Gott time machine, originally constructed for
the case of vanishing cosmological constant, provides a precise mechanism for
black hole formation. As a result, one obtains an exact analytic understanding
of the Choptuik scaling.Comment: 6 pages, Late
Curvature singularity of the distributional BTZ black hole geometry
For the non-rotating BTZ black hole, the distributional curvature tensor
field is found. It is shown to have singular parts proportional to a
-distribution with support at the origin. This singularity is related,
through Einstein field equations, to a point source. Coordinate invariance and
independence on the choice of differentiable structure of the results are
addressed.Comment: Latex, 7 page
Thermodynamics and Evaporation of the 2+1-D Black Hole
The properties of canonical and microcanonical ensembles of a black hole with
thermal radiation and the problem of black hole evaporation in 3-D are studied.
In 3-D Einstein-anti-de Sitter gravity we have two relevant mass scales,
, and , which are particularly relevant
for the evaporation problem. It is argued that in the `weak coupling' regime
, the end point of an evaporating black hole formed
with an initial mass , is likely to be a stable remnant in equilibrium
with thermal radiation. The relevance of these results for the information
problem and for the issue of back reaction is discussed. In the `strong
coupling' regime, a full fledged quantum gravity
treatment is required. Since the total energy of thermal states in anti-de
Sitter space with reflective boundary conditions at spatial infinity is bounded
and conserved, the canonical and microcanonical ensembles are well defined. For
a given temperature or energy black hole states are locally stable. In the weak
coupling regime black hole states are more probable then pure radiation states.Comment: 11 pages, TAUP 2141/94, Late
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