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Titel:
Fractal geometry of spin-glass models
Author(s):
J. Fernando Fontanari,
Peter F. Stadler,
Phys.Rev.Lett. submitted (2001)
Abstract:
Stability and diversity are two key properties that living entities share
with spin glasses, where they are manifested through the breaking of the
phase space into many valleys or local minima connected by saddle
points. The topology of the phase space can be conveniently condensed into
a tree structure, akin to the biological phylogenetic trees, whose tips are
the local minima and internal nodes are the lowest-energy saddles
connecting those minima. For the infinite-range Ising spin glass with
p-spin interactions, we show that the average size-frequency
distribution of saddles obeys a power law <P(w)> ~
w-D, where w=w(s) is the number of minima that can be
connected through saddle s, and D is the fractal dimension of
the phase space.
Keywords:
spin glasses, landscapes, barrier trees, fractals
Return to 2001 working papers list.