G. Gaeta
Replica theory and the geometry of symmetry breaking
(31K, Plain TeX)
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.