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On Phase Transitions for -Adic Potts Model with Competing Interactions on a Cayley Tree
Farrukh Mukhamedov, Utkir Rozikov, Jose Fernando F. Mendes
In the paper we considere three state -adic Potts model with competing interactions on a Cayley tree of order two. We reduce a problem of describing of the -adic Gibbs measur…
k-core organization of complex networks
S. N. Dorogovtsev, A. V. Goltsev, J. F. F. Mendes
We analytically describe the architecture of randomly damaged uncorrelated networks as a set of successively enclosed substructures -- k-cores. The k-core is the largest subgraph w…
Correlations in interacting systems with a network topology
S. N. Dorogovtsev, A. V. Goltsev, J. F. F. Mendes
We study pair correlations in cooperative systems placed on complex networks. We show that usually in these systems, the correlations between two interacting objects (e.g., spins),…
Organization of complex networks without multiple connections
S. N. Dorogovtsev, J. F. F. Mendes, A. M. Povolotsky +1
We find a new structural feature of equilibrium complex random networks without multiple and self-connections. We show that if the number of connections is sufficiently high, these…