The Griffiths Phase on Hierarchical Modular Networks with Small-world Edges

Abstract

The Griffiths phase has been proposed to induce a stretched critical regime that facilitates self-organizing of brain networks for optimal function. This phase stems from the intrinsic structural heterogeneity of brain networks, such as the hierarchical modular structure. In this work, we extend this concept to modified hierarchical networks with small-world connections based on Hanoi networks. Through extensive simulations, we identify the role of an exponential distribution of the inter-moduli connectivity probability across hierarchies determining the emergence of the Griffiths phase. Numerical results and the complementary spectral analysis on the relevant networks can be helpful for a deeper understanding of the essential structural characteristics of finite dimensional networks to support the Griffiths phase.

7 pages, 7 figures

References in corpus (11)

• Rare region effects at classical, quantum, and non-equilibrium phase transitions
• Epidemic thresholds of the Susceptible-Infected-Susceptible model on networks: A comparison of numerical and theoretical results
• Griffiths phases on complex networks
• Quantum Griffiths effects in itinerant Heisenberg magnets
• Small-World Bonds and Patchy Percolation on the Hanoi Network
• Hierarchical, Regular Small-World Networks
• Percolation quantum phase transitions in diluted magnets
• Slow dynamics and rare-region effects in the contact process on weighted tree networks
• Localization transition, Lifschitz tails and rare-region effects in network models
• From explosive to infinite-order transitions on a hyperbolic network
• Evaluation of Spectral Zeta-Functions with the Renormalization Group