From Micro to Macro The Bottom-Up Approach

8 Confirm that the Bleaney-Bowers expression for a dimer with 5 equals 

This is rather trivial as long as dimeric systems are concerned, because there is actually only one parameter in the analytical expression of x and no new information is obtained by calculating x (T) from the theoretical estimates of the T-value. The situation is different when polynuclear systems are considered. Most importantly, there are not many systems for which an exact expression of x has been derived. In addition to the above stated expression for binuclear complexes, Boca derived expression for tri- and tetra-nuclear systems [3], which turn out to be rather lengthy. The situation is even more complicated for extended systems, which have (in principle) an infinite number of interacting magnetic centers. 

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 

More general expressions were derived by Curely for S 1/2, for 2D lattices with different magnetic interaction paths (Fig. 3.7 middle) and to hexagonal (or honeycomb) lattices (Fig. 3.7 right) [10, 11]. 

8 Periodic boundaries in a one-dimensional chain. The central unit of five magnetic centers is repeated on the left and the right by introducing the interaction between center 1 and 5. The actual model is a closed ring of five centers 

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