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Non-equilibrium phase transition and cluster size distribution in aggregation and weighted-fragmentation processes

Author

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  • Sekiyama, Makoto
  • Ohtsuki, Toshiya
  • Yamamoto, Hiroshi

Abstract

Through numerical simulations, we investigate the influence of an index ϕ on the cluster size distribution in aggregation and weighted-fragmentation processes where a decomposed cluster of size a is selected with a power-law weight W(a)∝aϕ. We reveal the existence of a non-equilibrium phase transition from an exponentially decayed phase to a partially condensed phase and calculate the threshold ϕc for this phase transition. For ϕ>ϕc, cluster size distribution asymptotically obeys exponential decay, which results in the largest cluster sized on the order of lnN, where N is a total cluster number. Exponential decay rates are computed as a function of ϕ. It is notable that the curvature of the distribution changes its sign at ϕ=1. For ϕ<ϕc, a partially condensed phase takes place and one big cluster sized on the order of a total monomer number M emerges and coexists with small clusters.

Suggested Citation

  • Sekiyama, Makoto & Ohtsuki, Toshiya & Yamamoto, Hiroshi, 2022. "Non-equilibrium phase transition and cluster size distribution in aggregation and weighted-fragmentation processes," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 599(C).
    • Handle: RePEc:eee:phsmap:v:599:y:2022:i:c:s0378437122003156
    DOI: 10.1016/j.physa.2022.127425
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    References listed on IDEAS

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    1. Hiroshi Yamamoto & Toshiya Ohtsuki & Akihiro Fujihara & Satoshi Tanimoto & Keizo Yamamoto & Sasuke Miyazima, 2005. "Asymptotic analysis of the model for distribution of high-tax payers," Papers cond-mat/0510693, arXiv.org, revised Oct 2007.
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