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We have studied the topology of the energy landscape of a
spin-glass model and the effect of frustration on it by looking at
the connectivity and disconnectivity graphs of the inherent
structure. The connectivity network shows the adjacency of energy
minima whereas the disconnectivity network tells us about the
heights of the energy barriers. Both graphs are constructed by the
exact enumeration of a two-dimensional square lattice of a
frustrated spin glass with nearest-neighbor interactions up to the
size of 27 spins. The enumeration of the energy-landscape minima
as well as the analytical mean-field approximation show that these
minima have a Gaussian distribution, and the connectivity graph
has a log-Weibull degree distribution of shape $\kappa=8.22$ and
scale $\lambda=4.84$. To study the effect of frustration on these
results, we introduce an unfrustrated spin-glass model and
demonstrate that the degree distribution of its connectivity graph
shows a power-law behavior with the $-3.46$ exponent, which is
similar to the behavior of proteins and Lennard-Jones clusters in
its power-law form.
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