97-614 G. Gaeta

Replica theory and the geometry of symmetry breaking (31K, Plain TeX) Dec 7, 97

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Abstract. In the study of Replica Symmetry Breaking (RSB), one is led to consider functions F of pseudomatrices, i.e. of matrices of order P, with P a real, rather than an integer, number. We propose a mathematically rigorous definition of pseudomatrices, and show that from this it follows that the minimum of F over the space of pseudomatrices Q(x,y) which depend only on (x-y) is also a critical point for F; this corresponds to a property which is usually assumed without proof in the study of RSB. We also find that generic bifurcations from such a minimum lead to minima corresponding to periodic quasimatrices. These results are obtained through use of Michel's theory of symmetry breaking.

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