522 research outputs found
Function theory on metabelian solvmanifold
AbstractThe Laplace operators for metabelian solvmanifolds are used to describe certain spaces of C∞ functions on metabelian solvmanifolds of interest in harmonic analysis
Large-D Expansion from Variational Perturbation Theory
We derive recursively the perturbation series for the ground-state energy of
the D-dimensional anharmonic oscillator and resum it using variational
perturbation theory (VPT). From the exponentially fast converging approximants,
we extract the coefficients of the large-D expansion to higher orders. The
calculation effort is much smaller than in the standard field-theoretic
approach based on the Hubbard-Stratonovich transformation.Comment: Author Information under http://hbar.wustl.edu/~sbrandt and
http://www.theo-phys.uni-essen.de/tp/ags/pelster_di
Mastering the Master Field
The basic concepts of non-commutative probability theory are reviewed and
applied to the large limit of matrix models. We argue that this is the
appropriate framework for constructing the master field in terms of which large
theories can be written. We explicitly construct the master field in a
number of cases including QCD. There we both give an explicit construction
of the master gauge field and construct master loop operators as well. Most
important we extend these techniques to deal with the general matrix model, in
which the matrices do not have independent distributions and are coupled. We
can thus construct the master field for any matrix model, in a well defined
Hilbert space, generated by a collection of creation and annihilation
operators---one for each matrix variable---satisfying the Cuntz algebra. We
also discuss the equations of motion obeyed by the master field.Comment: 46 pages plus 11 uuencoded eps figure
Critical phenomena and quantum phase transition in long range Heisenberg antiferromagnetic chains
Antiferromagnetic Hamiltonians with short-range, non-frustrating interactions
are well-known to exhibit long range magnetic order in dimensions,
but exhibit only quasi long range order, with power law decay of correlations,
in d=1 (for half-integer spin). On the other hand, non-frustrating long range
interactions can induce long range order in d=1. We study Hamiltonians in which
the long range interactions have an adjustable amplitude lambda, as well as an
adjustable power-law , using a combination of quantum Monte Carlo
and analytic methods: spin-wave, large-N non-linear sigma model, and
renormalization group methods. We map out the phase diagram in the lambda-alpha
plane and study the nature of the critical line separating the phases with long
range and quasi long range order. We find that this corresponds to a novel line
of critical points with continuously varying critical exponents and a dynamical
exponent, z<1.Comment: 27 pages, 12 figures. RG flow added. Final version to appear in JSTA
The stability of a cubic fixed point in three dimensions from the renormalization group
The global structure of the renormalization-group flows of a model with
isotropic and cubic interactions is studied using the massive field theory
directly in three dimensions. The four-loop expansions of the \bt-functions
are calculated for arbitrary . The critical dimensionality and the stability matrix eigenvalues estimates obtained on the basis of
the generalized Pad-Borel-Leroy resummation technique are shown
to be in a good agreement with those found recently by exploiting the five-loop
\ve-expansions.Comment: 18 pages, LaTeX, 5 PostScript figure
Quark Confinement in the Deconfined Phase
In cylindrical volumes with C-periodic boundary conditions in the long
direction, static quarks are confined even in the gluon plasma phase due to the
presence of interfaces separating the three distinct high-temperature phases.
An effective "string tension" is computed analytically using a dilute gas of
interfaces. At T_c, the deconfined-deconfined interfaces are completely wet by
the confined phase and the high-temperature "string tension" turns into the
usual string tension below T_c. Finite size formulae are derived, which allow
to extract interface and string tensions from the expectation value of a single
Polyakov loop. A cluster algorithm is built for the 3-d three-state Potts model
and an improved estimator for the Polyakov loop is constructed, based on the
number of clusters wrapping around the C-periodic direction of the cluster.Comment: 3 pages, Latex, talk presented at Lattice '97, to appear in Nucl.
Phys. B (Proc. Suppl.), uses espcrc2.st
Thurston equivalence of topological polynomials
We answer Hubbard's question on determining the Thurston equivalence class of
``twisted rabbits'', i.e. images of the ``rabbit'' polynomial under n-th powers
of the Dehn twists about its ears.
The answer is expressed in terms of the 4-adic expansion of n. We also answer
the equivalent question for the other two families of degree-2 topological
polynomials with three post-critical points.
In the process, we rephrase the questions in group-theoretical language, in
terms of wreath recursions.Comment: 40 pages, lots of figure
Antiferromagnetic 4-d O(4) Model
We study the phase diagram of the four dimensional O(4) model with first
(beta1) and second (beta2) neighbor couplings, specially in the beta2 < 0
region, where we find a line of transitions which seems to be second order. We
also compute the critical exponents on this line at the point beta1 =0 (F4
lattice) by Finite Size Scaling techniques up to a lattice size of 24, being
these exponents different from the Mean Field ones.Comment: 26 pages LaTeX2e, 7 figures. The possibility of logarithmic
corrections has been considered, new figures and tables added. Accepted for
publication in Physical Review
The Large- Limit of the Two-Hermitian-matrix model by the hidden BRST method
This paper discusses the large N limit of the two-Hermitian-matrix model in
zero dimensions, using the hidden BRST method. A system of integral equations
previously found is solved, showing that it contained the exact solution of the
model in leading order of large .Comment: 19 pages, Latex,CERN--TH-6531/9
Critical exponents from parallel plate geometries subject to periodic and antiperiodic boundary conditions
We introduce a renormalized 1PI vertex part scalar field theory setting in
momentum space to computing the critical exponents and , at least
at two-loop order, for a layered parallel plate geometry separated by a
distance L, with periodic as well as antiperiodic boundary conditions on the
plates. We utilize massive and massless fields in order to extract the
exponents in independent ultraviolet and infrared scaling analysis,
respectively, which are required in a complete description of the scaling
regions for finite size systems. We prove that fixed points and other critical
amounts either in the ultraviolet or in the infrared regime dependent on the
plates boundary condition are a general feature of normalization conditions. We
introduce a new description of typical crossover regimes occurring in finite
size systems. Avoiding these crossovers, the three regions of finite size
scaling present for each of these boundary conditions are shown to be
indistinguishable in the results of the exponents in periodic and antiperiodic
conditions, which coincide with those from the (bulk) infinite system.Comment: Modified introduction and some references; new crossover regimes
discussion improved; Appendixes expanded. 48 pages, no figure
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