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We have *N* spins , *i*=1, 2,... on a lattice with
coordinate number *z*. Each spin can be either up or
down^{}:

- 1.
- Each spin interacts with
*external field**H*: - 2.
- Each pair of neighbors interacts:
- (a)
- Parallel spins are favored--energy -
*J*,*J*>0 - (b)
- Antiparallel spins are discouraged--energy +
*J*

*i*,*j*) means*sum over all pairs of nearest neighbors*

(1) |

Microscopic state of the system--combination of all spins:

Partition function: We don't have momenta here--this is actually a
Average magnetization (*H* is conjugated to !)

© 1997

Mon Oct 13 22:07:20 EDT 1997