Abstract
We study the network topology of the energy landscape in a spin-glass model, both analytically and numerically. We construct the network of adjacent minima and then, we show that this network has a log-normal degree distribution which is a consequence of the normal distribution of energy minima in spin-glasses.
To perform our study we use a 2D square lattice spin-glasses with nearest neighbor interaction up to the size of 27 spins. The size of the system lets us to enumerate all of its possible configurations. A mean field approximation also supports our numerical results.
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