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33646656452
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note
-
For the sake of clarity, a "hat" (̂) is used to distinguish operators from numbers.
-
-
-
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33
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33646643165
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-
note
-
The prime in the summation indicates that the terms with α=β and σ=σ′ are excluded. For simplicity we neglect in Eqs. (2) and (3) the dependence of the d-level energies and Coulomb integrals on the orbital α, retaining the dominant spin dependence due to exchange.
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33646646462
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Ph.D thesis, Freie Universität Berlin, (unpublished)
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G. M. Pastor, Ph.D thesis, Freie Universität Berlin, 1989 (unpublished).
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Pastor, G.M.1
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43
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33646652917
-
-
note
-
BT ln Q associated to the many-body Hamiltonian H given by Eqs. (1)-(3).
-
-
-
-
44
-
-
33646639422
-
-
note
-
More recent applications of the mean-field approach to TM clusters and nanostructures at T=0 may be found, for example, in Refs. 18 and 32, and in references therein.
-
-
-
-
46
-
-
33646638870
-
-
note
-
l≥0-or equivalently positive values of the total cluster moment-must be applied to avoid trivially vanishing results for the average magnetization due to time-inversion symmetry. This corresponds to the experimental situation where the cluster moment is aligned along an external magnetic field.
-
-
-
-
48
-
-
33646665982
-
-
note
-
0 at the cluster surface due to charge transfer effects (see Ref. 15). This is consistent with other calculations.
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-
-
-
49
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0242323625
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edited by C. Domb and M. S. Green (Academic, London)
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P. G. Watson, Phase Transitions and Critical Phenomena, edited by C. Domb and M. S. Green (Academic, London, 1972), Vol. 2, p. 101; M. N. Barber, Phase Transitions and Critical Phenomena, edited by G. Domb and J. L. Lebowitz (Academic, London, 1983), Vol. 8, p. 145.
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P. G. Watson, Phase Transitions and Critical Phenomena, edited by C. Domb and M. S. Green (Academic, London, 1972), Vol. 2, p. 101; M. N. Barber, Phase Transitions and Critical Phenomena, edited by G. Domb and J. L. Lebowitz (Academic, London, 1983), Vol. 8, p. 145.
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Barber, M.N.1
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