Stochastic Processes on a Lattice and Gibbs Measures: Mathematical Physics Studies, cartea 11
Autor Bernard Prum, Jean Claude Forten Limba Engleză Hardback – 30 dec 1990
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Specificații
ISBN-13: 9780792310693
ISBN-10: 0792310691
Pagini: 220
Dimensiuni: 155 x 235 x 14 mm
Greutate: 0.51 kg
Ediția:1991
Editura: SPRINGER NETHERLANDS
Colecția Springer
Seria Mathematical Physics Studies
Locul publicării:Dordrecht, Netherlands
ISBN-10: 0792310691
Pagini: 220
Dimensiuni: 155 x 235 x 14 mm
Greutate: 0.51 kg
Ediția:1991
Editura: SPRINGER NETHERLANDS
Colecția Springer
Seria Mathematical Physics Studies
Locul publicării:Dordrecht, Netherlands
Public țintă
ResearchDescriere
In
many
domains
one
encounters
"systems"
of
interacting
elements,
elements
that
interact
more
forcefully
the
closer
they
may
be.
The
historical
example
upon
which
the
theory
offered
in
this
book
is
based
is
that
of
magnetization
as
it
is
described
by
the
Ising
model.
At
the
vertices
of
a
regular
lattice
of
sites,
atoms
"choos
e"
an
orientation
under
the
influence
of
the
orientations
of
the
neighboring
atoms.
But
other
examples
are
known,
in
physics
(the
theories
of
gasses,
fluids,
..
J,
in
biology
(cells
are
increasingly
likely
to
become
malignant
when
their
neighboring
cells
are
malignant),
or
in
medecine
(the
spread
of
contagious
deseases,
geogenetics,
..
.),
even
in
the
social
sciences
(spread
of
behavioral
traits
within
a
population).
Beyond
the
spacial
aspect
that
is
related
to
the
idea
of
"neighboring"
sites,
the
models
for
all
these
phenomena
exhibit
three
common
features:
-
The
unavoidable
ignorance
about
the
totality
of
the
phenomenon
that
is
being
studied
and
the
presence
of
a
great
number
of
often
unsuspected
factors
that
are
always
unquantified
lead
inevitably
to
stochastic
models.
The
concept
of
accident
is
very
often
inherent
to
the
very
nature
of
the
phenomena
considered,
so,
to
justify
this
procedure,
one
has
recourse
to
the
physicist's
principle
of
indeterminacy,
or,
for
example,
to
the
factor
of
chance
in
the
Mendelian
genetics
of
phenotypes.
Cuprins
1
—
Aspects
of
the
Ising
Model.-
1.
Introduction.-
2.
Peieris’s
Argument.-
3.
Imposed
Field,
Thermodynamic
Quantities.-
4.
The
Unidimensional
Case
and
Tree.-
5.
Antiferromagnetism.-
2
—
Gibbs
Measures.-
1.
The
DLR
Problem.-
2.
The
Structure
of
G.-
3.
Gibbs
Specifications,
Gibbs
Measures.-
4.
Relations
with
Thermodynamics.-
3
—
The
Existence
of
Gibbs
Measures.-
1.
Markovian
Properties.-
2.
Existence
of
Gibbs
Measures
when
?
is
Finite.-
3.
Existence
of
Gibbs
Measures
—
the
General
Case.-
4.
Models
of
the
P(?)-Type,
Gaussian
Gibbs
Measures
S.-
4
—
Phase
Transitions
—
1:
Methods
of
Convex
Analysis.-
1.
Holley’s
Inequality.-
2.
The
FKG
Inequality.-
3.
Attracting
Specifications.-
4.
The
Ising
Model
on
?2.-
5.
Symmetry
Breaking
on
?d
for
d
?
3.-
5
—
Other
Inequalities.-
1.
Urse11
Functions.-
2.
GK
S
Inequalities.-
3.
The
GHS
Inequality.-
4.
The
Simon-Lieb
Inequality.-
S.
Additional
Inequalities.-
6
—
Phase
Transitions
—
2:
Phase
Diagrams
and
Perturbed
Hamiltonians.-
1.
Fundamental
Configurations.-
2.
Perturbed
Hamiltonians.-
3.
The
Pirogov-Sinaï
Theorem.-
4.
Boundary
Models.-
S.
Principle
of
the
Proof.-
7
—
Phase
Transitions
—
3:
Positive
Reflexivity.-
1.
Reflexive
Positivity.-
2.
The
Unidimensional
Case.-
3.
Checkerboard
Estimate.-
4.
Gaussian
Domination.-
5.
The
Infrared
Domination.-
8
—
Continuous
Symmetry
and
Other
Methods.-
1.
The
Case
of
Continuous
Symmetry.-
2.
The
Lack
of
Symmetry
Breaking
when
d
=
2.-
3.
Spontaneous
Magnetization
when
d
?
3.-
4.
Onsager
s
Method.-
5.
Combinatorial
Approach.-
6.
The
Lee-Yang
Theorem.-
9
—
The
Dynamics
of
Ising
Systems.-
1.
Introduction.-
2.
A
Finite
Number
of
Sites.-
3.
An
Infinite
Number
of
Sites.-
10
—
Statistics
and
Applications.-
1.
Ergodicity.-
2.
Statistics.-
3.
Image
Processing.-
4.
Other
Applications.