616,412 research outputs found
Some Applications of the Lee-Yang Theorem
For lattice systems of statistical mechanics satisfying a Lee-Yang property
(i.e., for which the Lee-Yang circle theorem holds), we present a simple proof
of analyticity of (connected) correlations as functions of an external magnetic
field h, for Re h > 0 or Re h < 0. A survey of models known to have the
Lee-Yang property is given. We conclude by describing various applications of
the aforementioned analyticity in h.Comment: 16 page
Lee, Joseph H.
John J. Brice as I knew Him. Recollections of army career officer and music instructor, Joseph Lee about a young army recruit, John Brice, stationed at Camp Furlong in Columbus, New Mexico and later becoming in charge of ROTC at Howard University.https://dh.howard.edu/og_manusripts/1015/thumbnail.jp
Peggy H. Lee
A Virginia native and graduate of Virginia Tech, Peggy H. Lee began her career in restaurant management, but soon switched to school food service. She first worked as a supervisor of twenty-two schools in the Norfolk school system and then became the nutritionist for Virginia Beach Schools. From Virginia Beach she moved to Norfolk as a supervisor and then took the director’s position in Chesapeake. After thirty years of service she retired and now works for the National Dairy Council.https://egrove.olemiss.edu/icn_ohistories/1080/thumbnail.jp
Lee County 4-H Delegates
Lee County 4-H Delegates on Lee Hall stepshttps://scholarsjunction.msstate.edu/ua-photo-collection/9140/thumbnail.jp
Novel Spin and Statistical Properties of Nonabelian Vortices
We study the statistics of vortices which appear in (2+1)--dimensional
spontaneously broken gauge theories, where a compact group G breaks to a finite
nonabelian subgroup H. Two simple models are presented. In the first, a quantum
state which is symmetric under the interchange of a pair of indistinguishable
vortices can be transformed into an antisymmetric state after the passage
through the system of a third vortex with an appropriate -flux element.
Further, there exist states containing two indistinguishable spinless vortices
which obey Fermi statistics. These results generalize to loops of nonabelian
cosmic string in 3+1 dimensions. In the second model, fractional analogues of
the above behaviors occur. Also, composites of vortices in this theory may
possess fractional ``Cheshire spin'' which can be changed by passing an
additional vortex through the system.Comment: 11 pages, UICHEP-TH/92-15; FERMILAB-PUB-92/233-T; SLAC-PUB-588
Yang-Lee Zeros of the Ising model on Random Graphs of Non Planar Topology
We obtain in a closed form the 1/N^2 contribution to the free energy of the
two Hermitian N\times N random matrix model with non symmetric quartic
potential. From this result, we calculate numerically the Yang-Lee zeros of the
2D Ising model on dynamical random graphs with the topology of a torus up to
n=16 vertices. They are found to be located on the unit circle on the complex
fugacity plane. In order to include contributions of even higher topologies we
calculated analytically the nonperturbative (sum over all genus) partition
function of the model Z_n = \sum_{h=0}^{\infty} \frac{Z_n^{(h)}}{N^{2h}} for
the special cases of N=1,2 and graphs with n\le 20 vertices. Once again the
Yang-Lee zeros are shown numerically to lie on the unit circle on the complex
fugacity plane. Our results thus generalize previous numerical results on
random graphs by going beyond the planar approximation and strongly indicate
that there might be a generalization of the Lee-Yang circle theorem for
dynamical random graphs.Comment: 19 pages, 7 figures ,1 reference and a note added ,To Appear in
Nucl.Phys
Reconfiguring Graph Homomorphisms on the Sphere
Given a loop-free graph , the reconfiguration problem for homomorphisms to
(also called -colourings) asks: given two -colourings of of a
graph , is it possible to transform into by a sequence of
single-vertex colour changes such that every intermediate mapping is an
-colouring? This problem is known to be polynomial-time solvable for a wide
variety of graphs (e.g. all -free graphs) but only a handful of hard
cases are known. We prove that this problem is PSPACE-complete whenever is
a -free quadrangulation of the -sphere (equivalently, the plane)
which is not a -cycle. From this result, we deduce an analogous statement
for non-bipartite -free quadrangulations of the projective plane. This
include several interesting classes of graphs, such as odd wheels, for which
the complexity was known, and -chromatic generalized Mycielski graphs, for
which it was not.
If we instead consider graphs and with loops on every vertex (i.e.
reflexive graphs), then the reconfiguration problem is defined in a similar way
except that a vertex can only change its colour to a neighbour of its current
colour. In this setting, we use similar ideas to show that the reconfiguration
problem for -colourings is PSPACE-complete whenever is a reflexive
-free triangulation of the -sphere which is not a reflexive triangle.
This proof applies more generally to reflexive graphs which, roughly speaking,
resemble a triangulation locally around a particular vertex. This provides the
first graphs for which -Recolouring is known to be PSPACE-complete for
reflexive instances.Comment: 22 pages, 9 figure
Location of the Lee-Yang zeros and absence of phase transitions in some Ising spin systems
We consider a class of Ising spin systems on a set \Lambda of sites. The
sites are grouped into units with the property that each site belongs to either
one or two units, and the total internal energy of the system is the sum of the
energies of the individual units, which in turn depend only on the number of up
spins in the unit. We show that under suitable conditions on these interactions
none of the |\Lambda| Lee-Yang zeros in the complex z = exp{2\beta h} plane,
where \beta is the inverse temperature and h the uniform magnetic field, touch
the positive real axis, at least for large values of \beta. In some cases one
obtains, in an appropriately taken \beta to infinity limit, a gas of hard
objects on a set \Lambda'; the fugacity for the limiting system is a rescaling
of z and the Lee-Yang zeros of the new partition function also avoid the
positive real axis. For certain forms of the energies of the individual units
the Lee-Yang zeros of both the finite- and zero-temperature systems lie on the
negative real axis for all \beta. One zero-temperature limit of this type, for
example, is a monomer-dimer system; our results thus generalize, to finite
\beta, a well-known result of Heilmann and Lieb that the Lee-Yang zeros of
monomer-dimer systems are real and negative.Comment: Plain TeX. Seventeen pages, five figures from .eps files. Version 2
corrects minor errors in version
On localization of the Schr\"odinger maximal operator
In \cite{Lee:2006:schrod-converg}, when the spatial variable is
localized, Lee observed that the Schr\"odinger maximal operator
enjoys certain localization property in for frequency
localized functions. In this note, we give an alternative proof of this
observation by using the method of stationary phase, and then include two
applications: the first is on is on the equivalence of the local and the global
Schr\"odinger maximal inequalities; secondly the local Schr\"odinger maximal
inequality holds for , which implies that
converges to almost everywhere if . These results are not
new. In this note we would like to explore them from a slightly different
perspective, where the analysis of the stationary phase plays an important
role.Comment: 14 pages, no figure. Note
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