10,871 research outputs found
Explicit minimal Scherk saddle towers of arbitrary even genera in
Starting from works by Scherk (1835) and by Enneper-Weierstra\ss \ (1863),
new minimal surfaces with Scherk ends were found only in 1988 by Karcher (see
\cite{Karcher1,Karcher}). In the singly periodic case, Karcher's examples of
positive genera had been unique until Traizet obtained new ones in 1996 (see
\cite{Traizet}). However, Traizet's construction is implicit and excludes {\it
towers}, namely the desingularisation of more than two concurrent planes. Then,
new explicit towers were found only in 2006 by Martin and Ramos Batista (see
\cite{Martin}), all of them with genus one. For genus two, the first such
towers were constructed in 2010 (see \cite{Valerio2}). Back to 2009, implicit
towers of arbitrary genera were found in \cite{HMM}. In our present work we
obtain {\it explicit} minimal Scherk saddle towers, for any given genus ,
Hierarchical Mean-Field Theories in Quantum Statistical Mechanics
We present a theoretical framework and a calculational scheme to study the
coexistence and competition of thermodynamic phases in quantum statistical
mechanics. The crux of the method is the realization that the microscopic
Hamiltonian, modeling the system, can always be written in a hierarchical
operator language that unveils all symmetry generators of the problem and,
thus, possible thermodynamic phases. In general one cannot compute the
thermodynamic or zero-temperature properties exactly and an approximate scheme
named ``hierarchical mean-field approach'' is introduced. This approach treats
all possible competing orders on an equal footing. We illustrate the
methodology by determining the phase diagram and quantum critical point of a
bosonic lattice model which displays coexistence and competition between
antiferromagnetism and superfluidity.Comment: 4 pages, 2 psfigures. submitted Phys. Rev.
The dimerized phase of ionic Hubbard models
We derive an effective Hamiltonian for the ionic Hubbard model at half
filling, extended to include nearest-neighbor repulsion. Using a spin-particle
transformation, the effective model is mapped onto simple spin-1 models in two
particular cases. Using another spin-particle transformation, a slightly
modified model is mapped into an SU(3) antiferromagnetic Heisenberg model whose
exact ground state is known to be spontaneously dimerized. From the effective
models several properties of the dimerized phase are discussed, like
ferroelectricity and fractional charge excitations. Using bosonization and
recent developments in the theory of macroscopic polarization, we show that the
polarization is proportional to the charge of the elementary excitations
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