Finite-size scaling in complex networks

Abstract

A finite-size-scaling (FSS) theory is proposed for various models in complex networks. In particular, we focus on the FSS exponent, which plays a crucial role in analyzing numerical data for finite-size systems. Based on the droplet-excitation (hyperscaling) argument, we conjecture the values of the FSS exponents for the Ising model, the susceptible-infected-susceptible model, and the contact process, all of which are confirmed reasonably well in numerical simulations.

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• Percolation transition in networks with degree-degree correlation
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• Multiple phase transitions of the susceptible-infected-susceptible epidemic model on complex networks
• Critical fluctuations in spatial complex networks
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• Biased Percolation on Scale-free Networks
• Finite-size scaling, dynamic fluctuations, and hyperscaling relation in the Kuramoto model
• Critical behavior of the Ising model in annealed scale-free networks
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• Robustness and fragility of the susceptible-infected-susceptible epidemic models on complex networks
• Critical behavior of the contact process in annealed scale-free networks
• Critical behavior of the contact process on small-world networks
• The phase diagram and critical behavior of the three-state majority-vote model
• Macroscopic Time-Reversal Symmetry Breaking at Nonequilibrium Phase Transition
• Pair approximation for the $q$-voter model with independence on multiplex networks
• An overview of epidemic models with phase transitions to absorbing states running on top of complex networks
• Nature of synchronization transitions in random networks of coupled oscillators
• Nonequilibrium Zaklan model on Apollonian Networks
• Broad edge of chaos in strongly heterogeneous Boolean networks
• Percolation on bipartite scale-free networks
• Variability of Contact Process in Complex Networks
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• Fundamental Structural Constraint of Random Scale-Free Networks
• Independence role in the generalized Sznajd model
• Non-equilibrium mean-field theories on scale-free networks
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• The Diffusive Epidemic Process on Barabasi-Albert Networks
• Quantum Monte Carlo study of the transverse-field quantum Ising model on infinite-dimensional structures
• Ising model on a $restricted$ scale-free network
• Emergence of a finite-size-scaling function in the supervised learning of the Ising phase transition
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• $K$-selective percolation: A simple model leading to a rich repertoire of phase transitions
• Asymmetrically interacting spreading dynamics on complex layered networks
• Finite-size scaling in random $K$-satisfiability problems
• Three-state Majority-Vote Model on Barabási-Albert and Cubic Networks and the Unitary Relation for Critical Exponents
• Stochastic spreading processes on a network model based on regular graphs