Entropy, Specific Heat, Susceptibility, And Rushbrooke Inequality In Percolation

Abstract

We investigate percolation, a probabilistic model for continuous phase transition, on square and weighted planar stochastic lattices. In its thermal counterpart, entropy is minimally low where order parameter (OP) is maximally high and vice versa. In addition, specific heat, OP, and susceptibility exhibit power law when approaching the critical point and the corresponding critical exponents α,β,γ respectably obey the Rushbrooke inequality (RI) α+2β+γ≥2. Their analogs in percolation, however, remain elusive. We define entropy and specific heat and redefine susceptibility for percolation and show that they behave exactly in the same way as their thermal counterpart. We also show that RI holds for both the lattices albeit they belong to different universality classes.

Publication Date

11-7-2017

Publication Title

Physical Review E

Volume

96

Issue

5

Document Type

Article

Personal Identifier

scopus

DOI Link

https://doi.org/10.1103/PhysRevE.96.050101

Socpus ID

85033551223 (Scopus)

Source API URL

https://api.elsevier.com/content/abstract/scopus_id/85033551223

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