Non-uniform coupling model of the frustrated chromium-based ring Cr<sub>8</sub>Ni

Antkowiak, Michał; Kucharski, Łukasz; Kamieniarz, G.

doi:10.1051/epjconf/20147505007

Cited by 6 publications

(2 citation statements)

References 19 publications

(22 reference statements)

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Single-ion anisotropy plays the crucial role in investigations of single-molecule magnets and in many cases of anisotropic models some features analogous to LMLO are also observed [33,35,36,48,49]. However, in such cases the total spin is not a good quantum number, so the LMLO should be rather related to the total magnetization.…”

Section: Conclusion and Final Remarksmentioning

confidence: 99%

“…Moreover, it can be proved (in some cases numerically only) that larger, non-bipartite in general, analogous of bipartite systems still exhibit the LMLO [30][31][32]. Similarly, this effect is observed for anisotropic systems, but the total spin number S has to be replaced by the total magnetization M [33][34][35][36]. Reformulation of the LMT to include all these cases is a challenging task and to complete it, this theorem itself has to be 'revisited' and mathematical background must be meticulously examined.…”

Section: Introductionmentioning

confidence: 96%

See 1 more Smart Citation

The Lieb–Mattis theorem revisited

Florek¹

2018

Nanosystems: Phys. Chem. Math.

View full text Add to dashboard Cite

Simple formulation and a straightforward proof of the Lieb-Mattis theorem (LMT) do not indicate how powerful a tool it is. For more than fifty years, this theorem has been mainly discussed in its 'strong' form and applied mainly to many type of infinite spin lattices. It can be easily proved that in such cases, geometrically frustrated systems have to be excluded. However, it has been recently shown that the so-called 'weak' or general form of the LMT can be exploited considering some small, geometrically frustrated quantum spin systems. Moreover, many systems, which do not satisfy assumptions of the LMT, show identical features, including the level order characteristic for bipartite spin systems. It yields a question about possible generalizations or modifications of this theorem to involve a larger class of problems. To begin, algebraic aspects have to be understood with the invaluable role of the Perron-Frobenius theorem. The latter theorem is investigated, discussed, modified etc. in immense number of works. Many of them are important in physical applications and ways of reasoning they present can be exploited in different approaches to the LMT.

show abstract

Section: Conclusion and Final Remarksmentioning

confidence: 99%