Complex network growth model: Possible isomorphism between nonextensive statistical mechanics and random geometry
Abstract
In the realm of BoltzmannGibbs statistical mechanics, there are three well known isomorphic connections with random geometry, namely, (i) the KasteleynFortuin theorem, which connects the λ → 1 limit of the λstate Potts ferromagnet with bond percolation, (ii) the isomorphism, which connects the λ → 0 limit of the λstate Potts ferromagnet with random resistor networks, and (iii) the de Gennes isomorphism, which connects the n → 0 limit of the nvector ferromagnet with selfavoiding random walk in linear polymers. We provide here strong numerical evidence that a similar isomorphism appears to emerge connecting the energy qexponential distribution ∝ e q  β q ɛ (with q = 4 / 3 and β q ω 0 = 10 / 3) optimizing, under simple constraints, the nonadditive entropy S q with a specific geographic growth random model based on preferential attachment through exponentially distributed weighted links, ω 0 being the characteristic weight.
 Publication:

Chaos
 Pub Date:
 May 2022
 DOI:
 10.1063/5.0090864
 arXiv:
 arXiv:2205.00998
 Bibcode:
 2022Chaos..32e3126T
 Keywords:

 Condensed Matter  Statistical Mechanics
 EPrint:
 5 pages and 2 figures