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Critical Phenomena of the Generalized Epidemic Process
New Phys.: Sae Mulli 2019; 69: 649~654
Published online June 28, 2019;
© 2019 New Physics: Sae Mulli.

Meesoon HA*

Department of Physics Education, Chosun University, Gwangju 61452, Korea
Correspondence to:
Received May 6, 2019; Revised May 9, 2019; Accepted May 9, 2019.
cc This is an open-access article distributed under the terms of the Creative Commons Attribution Non-Commercial License ( which permits unrestricted non-commercial use, distribution, and reproduction in any medium, provided the original work is properly cited.
We investigate mixed-order critical phenomena of the generalized epidemic process (GEP) on random scale-free networks characterized by the power-law distribution $p_k \sim k^{-\alpha}$.The GEP is a minimal model of spreading behaviors. Near tricritical points (TCPs) derived by using the generating method, we numerically confirm the associated scaling exponents as functions of $\alpha$. In particular, we propose an extended finite-size scaling theory of the GEP and crossover scaling behaviors, which are also confirmed by using extensive Monte Carlo simulations. Our results show that near TCPs, the GEP is governed by two distinct length scales, whose nontrivial dependence on $\alpha$ leads to rich transition behaviors.
PACS numbers: 02.50.-r, 05.70.Jk, 64.60.-i, 89.75.Hc
Keywords: GEP, Extended finite-size scaling, Mixed-order transitions, Tricriticality, Crossover scaling

June 2019, 69 (6)
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