The use of product measures as a way of doing mean field theory is known since long. Here, this approach is situated in the context of hyperensembles. Doing so allows for a further generalisation of the mean field approximation. This Chapter discusses also the occurrence of phase transitions in mean field models and the implication that these models do not belong to the exponential family.
KeywordsIsing Model Phase Transition Temperature Field Approximation Exponential Family Counting Factor
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- 2.Bratteli, O., Robinson, D.: Operator Algebras and Quantum Statistical Mechanics. Vol I, II. 2nd edition. Springer, New York, Berlin (1997) Google Scholar
- 9.Stanley, H.: Phase Transitions and Critical Phenomena. Harper & Row (1971) Google Scholar
- 11.Van der Straeten, E., Naudts, J.: A one-dimensional model for theoretical analysis of single molecule experiments. J. Phys. A: Math. Gen. pp. 5715–5726 (2006) Google Scholar