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Entropy, specific heat, susceptibility, and Rushbrooke inequality in percolation

M. K. Hassan, D. Alam, Z. I. Jitu, and M. M. Rahman
Phys. Rev. E 96, 050101(R) – Published 7 November 2017

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+γ2. 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.

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  • Received 6 March 2017

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

©2017 American Physical Society

Physics Subject Headings (PhySH)

Statistical Physics & ThermodynamicsCondensed Matter, Materials & Applied Physics

Authors & Affiliations

M. K. Hassan1, D. Alam2, Z. I. Jitu1, and M. M. Rahman1

  • 1Department of Physics, University of Dhaka, Dhaka 1000, Bangladesh
  • 2Department of Physics, University of Central Florida, Orlando, Florida 32816, USA

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Issue

Vol. 96, Iss. 5 — November 2017

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