PHYSICAL ORIGIN OF MULTIPLE THREE AND FOUR SPIN (OR ATOMS) EXCHANGE IN QUANTUM SOLIDS WITH SOME CONSEQUENCES

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Abstract
The zero point motion of quantum solids gives a finite frequency of exchange for the atoms. Calculations based on two-body Jastrow functions giving essentially two-atom exchange, cannot describe correctly the true geometrical hard core correlations. A simple model of four hard spheres in a box shows that four-atom cyclic exchange can be much larger than two-atom exchange. We propose a new method taking into account the hard core correlations. This model applied to solid 3He leads to preponderant four-spin exchange in the b.c.c. phase as shown by the experimental results and to a ferromagnetic three-spin exchange in h.c.p. 3He or adsorbed 3He or cyclic three-atom permutation in h.c.p. solid H2

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