Product-Sum universality and Rushbrooke inequality in explosive percolation

Abstract

We study explosive percolation (EP) on Erdös-Rényi network for product rule (PR) and sum rule (SR). Initially, it was claimed that EP describes discontinuous phase transition, now it is well-accepted as a probabilistic model for thermal continuous phase transition (CPT). However, no model for CPT is complete unless we know how to relate its observable quantities with those of thermal CPT. To this end, we define entropy, specific heat, re-define susceptibility and show that they behave exactly like their thermal counterparts. We obtain the critical exponents $\nu ,\alpha ,\beta$ and $\gamma$ numerically and find that both PR and SR belong to the same universality class and they obey the Rushbrooke inequality.

arXiv comment5 pages, 4 captioned figures

References in corpus (26)

• Scaling and percolation in the small-world network model
• Recent advances in percolation theory and its applications
• "Explosive Percolation" Transition is Actually Continuous
• Self-organized adaptation of a simple neural circuit enables complex robot behaviour
• Impact of Single Links in Competitive Percolation -- How complex networks grow under competition
• Exact solution of site and bond percolation on small-world networks
• Explosive Percolation is Continuous, but with Unusual Finite Size Behavior
• Explosive percolation in scale-free networks
• Explosive percolation via control of the largest cluster
• Percolation Transitions in Scale-Free Networks under Achlioptas Process
• Explosive Percolation: Novel critical and supercritical phenomena
• Construction and Analysis of Random Networks with Explosive Percolation
• Local cluster aggregation models of explosive percolation
• Scaling behavior of explosive percolation on the square lattice
• Breaking of the site-bond percolation universality in networks
• Explosive site percolation and finite size hysteresis
• Explosive site percolation with a product rule
• Explosive Percolation: Unusual Transitions of a Simple Model
• New universality class in percolation on multifractal scale-free planar stochastic lattice
• About the fastest growth of Order Parameter in Models of Percolation
• Universality class of site and bond percolation on multi-multifractal scale-free planar stochastic lattice
• On entropy, specific heat, susceptibility and Rushbrooke inequality in percolation
• Inverting the Achlioptas rule for explosive percolation
• Information entropy of classical versus explosive percolation
• Criticality and Continuity of Explosive Site Percolation in Random Networks
• Explosive percolation on scale-free multifractal weighted planar stochastic lattice

Cited by in corpus (5)

• Bond percolation between $k$ separated points on a square lattice
• Explosive percolation in finite dimensions
• Redefinition of site percolation in light of entropy and the second law of thermodynamics
• Universality class of explosive percolation in Barabási-Albert networks
• Thermodynamic analysis of diverse percolation transitions