Heisenberg lattices

Symmetric group approach to the theory of Heisenberg lattices... 

Magnetic susceptibility data in two-dimensional extended systems are often interpreted based on the work of Rushbrooke and Wood [9], who derived an expression for X (T) valid for high temperatures. The discovery of the high Tc superconductors renewed the interest in the 2D Heisenberg lattices and the original work was extended to lower temperatures. A workable expression for a uniform lattice—characterized... 

In the earlier treatment we reached the conclusion that resonance absorption occurs at the Larmor precessional frequency, a conclusion implying that the absorption line has infinitesimal width. Actually NMR absorption bands have finite widths for several reasons, one of which is spin-lattice relaxation. According to the Heisenberg uncertainty principle, which can be stated... 

Vertex algebra from a lattice. It is known that a vertex algebra is construted from an even lattice L ([9, 20]). We briefly recall the construction. Let us denote by (-I-) the bilinear form of the lattice. Let be the Heisenberg Lie algebra associated with L, that is a Lie algebra generated by a n) a E L, n e Z 0 ) and K with relation... 

Spectral line width varies inversely with the excited-state lifetime according to Heisenbergs principle, AT X A H = hi 2n, where AT is the lifetime of the excited spin state, h is Planck s constant, and AH is the effective width of the absorption signal. Excited-state lifetimes are subject to environmental (including chemical) influences. The resulting line-shape changes yield information about the chemical environment of the Mn atoms. Both spin-lattice and spin-spin relaxation mechanisms can contribute to the overall lifetime. 

The theoretical model [130] was developed as an extension of the classical theory of dipolar broadening in dilute solid solutions in the absence of exchange interactions [16]. It was suggested in [130] how to determine the dipolar part in the line width by subtraction of the calculated input of Heisenberg exchange interaction of pairs of exchange-coupled ions. Equations were written for the three cubic lattices as a function of ion s concentration for various numbers of cationic sites included in a sphere of radius Rc with the assumption that clustering effects were absent. The results were compared well with experimental data on Cr3+ in MgO powders. 

In cases where Heisenberg Hamiltonian matrix dimensions prohibit their exact treatment one can use for energy states which are predominantly antiferromagnetic, an approximate method based on the idea of forming bonds between different lattice sites. These bonds, or rather the wave functions formed for these bonds, are then allowed to resonate giving rise to the RVB method mentioned earlier. The RVB method is very useful, since not only it makes possible a treatment of lattices which are out of reach by... 

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