 97614 G. Gaeta
 Replica theory and the geometry of symmetry breaking
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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 (xy) 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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