638 research outputs found
Hierarchic Superposition Revisited
Many applications of automated deduction require reasoning in first-order logic modulo background theories, in particular some form of integer arithmetic. A major unsolved research challenge is to design theorem provers that are "reasonably complete" even in the presence of free function symbols ranging into a background theory sort. The hierarchic superposition calculus of Bachmair, Ganzinger, and Waldmann already supports such symbols, but, as we demonstrate, not optimally. This paper aims to rectify the situation by introducing a novel form of clause abstraction, a core component in the hierarchic superposition calculus for transforming clauses into a form needed for internal operation. We argue for the benefits of the resulting calculus and provide two new completeness results: one for the fragment where all background-sorted terms are ground and another one for a special case of linear (integer or rational) arithmetic as a background theory
Superposition and chaining for totally ordered divisible abelian groups
We present a calculus for first-order theorem proving in the presence of the axioms of totally ordered divisible abelian groups. The calculus extends previous superposition or chaining calculi for divisible torsion-free abelian groups and dense total orderings without endpoints. As its predecessors, it is refutationally complete and requires neither explicit inferences with the theory axioms nor variable overlaps. It offers thus an efficient way of treating equalities and inequalities between additive terms over, e.g., the rational numbers within a first-order theorem prover
Quantum dynamics of the Neel vector in the antiferromagnetic molecular wheel CsFe8
The inelastic neutron scattering (INS) spectrum is studied for the
antiferromagnetic molecular wheel CsFe8, in the temperature range 2 - 60 K, and
for transfer energies up 3.6 meV. A qualitative analysis shows that the
observed peaks correspond to the transitions between the L-band states, from
the ground state up to the S = 5 multiplet. For a quantitative analysis, the
wheel is described by a microscopic spin Hamiltonian (SH), which includes the
nearest-neighbor Heisenberg exchange interactions and uniaxial easy-axis
single-ion anisotropy, characterized by the constants J and D, respectively.
For a best-fit determination of J and D, the L band is modeled by an effective
SH, and the effective SH concept extended such as to facilitate an accurate
calculation of INS scattering intensities, overcoming difficulties with the
dimension of the Hilbert space. The low-energy magnetism in CsFe8 is
excellently described by the generic SH used. The two lowest states are
characterized by a tunneling of the Neel vector, as found previously, while the
higher-lying states are well described as rotational modes of the Neel vector.Comment: 12 pages, 10 figures, REVTEX4, to appear in PR
Cancellative superposition decides the theory of divisible torsion-free abelian groups
In divisible torsion-free abelian groups, the efficiency of the cancellative superposition calculus can be greatly increased by combining it with a variable elimination algorithm that transforms every clause into an equivalent clause without unshielded variables. We show that the resulting calculus is a decision procedure for the theory of divisible torsion-free abelian groups
Ferromagnetic coupling and magnetic anisotropy in molecular Ni(II) squares
We investigated the magnetic properties of two isostructural Ni(II) metal
complexes [Ni4Lb8] and [Ni4Lc8]. In each molecule the four Ni(II) centers form
almost perfect regular squares. Magnetic coupling and anisotropy of single
crystals were examined by magnetization measurements and in particular by
high-field torque magnetometry at low temperatures. The data were analyzed in
terms of an effective spin Hamiltonian appropriate for Ni(II) centers. For both
compounds, we found a weak intramolecular ferromagnetic coupling of the four
Ni(II) spins and sizable single-ion anisotropies of the easy-axis type. The
coupling strengths are roughly identical for both compounds, whereas the
zero-field-splitting parameters are significantly different. Possible reasons
for this observation are discussed.Comment: 7 pages, 7 figure
Superposition with simplification as a decision procedure for the monadic class with equality
We show that strict superposition, a restricted form of paramodulation, can be combined with specifically designed simplification rules such that it becomes a decision procedure for the monadic class with equality. The completeness of the method follows from a general notion of redundancy for clauses and superposition inferences
Many-spin effects in inelastic neutron scattering and electron paramagnetic resonance of molecular nanomagnets
Many molecular magnetic clusters, such as single-molecule magnets, are
characterized by spin ground states with defined total spin S exhibiting
zero-field-splittings. In this work, the spectroscopic intensities of the
transitions within the ground-state multiplet are analyzed. In particular, the
effects of a mixing with higher-lying spin multiplets, which is produced by
anisotropic interactions and is neglected in the standard single-spin
description, are investigated systematically for the two experimental
techniques of inelastic neutron scattering (INS) and electron paramagnetic
resonance (EPR), with emphasis on the former technique. The spectroscopic
transition intensities are calculated analytically by constructing
corresponding effective spin operators perturbationally up to second order and
consequently using irreducible tensor operator techniques. Three main effects
of spin mixing are observed. Firstly, a pronounced dependence of the INS
intensities on the momentum transfer Q, with a typical oscillatory behavior,
emerges in first order, signaling the many-spin nature of the wave functions in
exchange-coupled clusters. Secondly, as compared to the results of a
first-order calculation, the intensities of the transitions within the spin
multiplet are affected differently by spin mixing. This allows one, thirdly, to
differentiate the higher-order contributions to the cluster magnetic anisotropy
which come from the single-ion ligand-field terms and spin mixing,
respectively. The analytical results are illustrated by means of the three
examples of an antiferromagnetic heteronuclear dimer, the Mn-[3 x 3] grid
molecule, and the single-molecule magnet Mn12.Comment: 18 pages, 3 figures, REVTEX4, to appear in PR
Exchange-coupling constants, spin density map, and Q dependence of the inelastic neutron scattering intensity in single-molecule magnets
The Q dependence of the inelastic neutron scattering (INS) intensity of
transitions within the ground-state spin multiplet of single-molecule magnets
(SMMs) is considered. For these transitions, the Q dependence is related to the
spin density map in the ground state, which in turn is governed by the
Heisenberg exchange interactions in the cluster. This provides the possibility
to infer the exchange-coupling constants from the Q dependence of the INS
transitions within the spin ground state. The potential of this strategy is
explored for the M = +-10 -> +- 9 transition within the S = 10 multiplet of the
molecule Mn12 as an example. The Q dependence is calculated for powder as well
as single-crystal Mn12 samples for various exchange-coupling situations
discussed in the literature. The results are compared to literature data on a
powder sample of Mn12 and to measurements on an oriented array of about 500
single-crystals of Mn12. The calculated Q dependence exhibits significant
variation with the exchange-coupling constants, in particular for a
single-crystal sample, but the experimental findings did not permit an
unambiguous determination. However, although challenging, suitable experiments
are within the reach of today's instruments.Comment: 11 pages, 6 figures, REVTEX4, to appear in PR
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