167,675 research outputs found
Cluster density functional theory for lattice models based on the theory of Mobius functions
Rosenfeld's fundamental measure theory for lattice models is given a rigorous
formulation in terms of the theory of Mobius functions of partially ordered
sets. The free-energy density functional is expressed as an expansion in a
finite set of lattice clusters. This set is endowed a partial order, so that
the coefficients of the cluster expansion are connected to its Mobius function.
Because of this, it is rigorously proven that a unique such expansion exists
for any lattice model. The low-density analysis of the free-energy functional
motivates a redefinition of the basic clusters (zero-dimensional cavities)
which guarantees a correct zero-density limit of the pair and triplet direct
correlation functions. This new definition extends Rosenfeld's theory to
lattice model with any kind of short-range interaction (repulsive or
attractive, hard or soft, one- or multi-component...). Finally, a proof is
given that these functionals have a consistent dimensional reduction, i.e. the
functional for dimension d' can be obtained from that for dimension d (d'<d) if
the latter is evaluated at a density profile confined to a d'-dimensional
subset.Comment: 21 pages, 2 figures, uses iopart.cls, as well as diagrams.sty
(included
Chain Decomposition Theorems for Ordered Sets (and Other Musings)
A brief introduction to the theory of ordered sets and lattice theory is
given. To illustrate proof techniques in the theory of ordered sets, a
generalization of a conjecture of Daykin and Daykin, concerning the structure
of posets that can be partitioned into chains in a ``strong'' way, is proved.
The result is motivated by a conjecture of Graham's concerning probability
correlation inequalities for linear extensions of finite posets
Electronic structures and magnetic orders of Fe-vacancies ordered ternary iron selenides TlFeSe and AFeSe (A=K, Rb, or Cs)
By the first-principles electronic structure calculations, we find that the
ground state of the Fe-vacancies ordered TlFeSe is a
quasi-two-dimensional collinear antiferromagnetic semiconductor with an energy
gap of 94 meV, in agreement with experimental measurements. This
antiferromagnetic order is driven by the Se-bridged antiferromagnetic
superexchange interactions between Fe moments. Similarly, we find that crystals
AFeSe (A=K, Rb, or Cs) are also antiferromagnetic semiconductors
but with a zero-gap semiconducting state or semimetallic state nearly
degenerated with the ground states. Thus rich physical properties and phase
diagrams are expected.Comment: Add results about AFeSe (A=K, Rb, or Cs);4 pages and 7
figure
Equality of bond percolation critical exponents for pairs of dual lattices
For a certain class of two-dimensional lattices, lattice-dual pairs are shown
to have the same bond percolation critical exponents. A computational proof is
given for the martini lattice and its dual to illustrate the method. The result
is generalized to a class of lattices that allows the equality of bond
percolation critical exponents for lattice-dual pairs to be concluded without
performing the computations. The proof uses the substitution method, which
involves stochastic ordering of probability measures on partially ordered sets.
As a consequence, there is an infinite collection of infinite sets of
two-dimensional lattices, such that all lattices in a set have the same
critical exponents.Comment: 10 pages, 7 figure
A variation principle for ground spaces
The ground spaces of a vector space of hermitian matrices, partially ordered
by inclusion, form a lattice constructible from top to bottom in terms of
intersections of maximal ground spaces. In this paper we characterize the
lattice elements and the maximal lattice elements within the set of all
subspaces using constraints on operator cones. Our results contribute to the
geometry of quantum marginals, as their lattices of exposed faces are
isomorphic to the lattices of ground spaces of local Hamiltonians.Comment: 18 pages, 2 figures, version v3 has an improved exposition, v4 has a
new non-commutative example and catches a glimpse of three qubit
Dynamic reorganization of vortex matter into partially disordered lattices
We report structural evidence of dynamic reorganization in vortex matter in
clean NbSe by joint small angle neutron scattering and ac-susceptibility
measurements. The application of oscillatory forces in a transitional region
near the order-disorder transition results in robust bulk vortex lattice
configurations with an intermediate degree of disorder. These
dynamically-originated configurations correlate with intermediate pinning
responses previously observed, resolving a long standing debate regarding the
origin of such responses.Comment: 9 pages, 7 figures. To be published in Physical Review Letter
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