Phase transitions in Schloegl's second model for autocatalysis on a Bethe lattice

Liu, Da-Jiang; Wang, Chi-Jen; Evans, James W.

doi:10.1103/physreve.104.014135

Phase transitions in Schloegl's second model for autocatalysis on a Bethe lattice

Journal Article · Mon Jul 26 00:00:00 EDT 2021 · Physical Review E

DOI:https://doi.org/10.1103/physreve.104.014135· OSTI ID:1817632

Liu, Da-Jiang ^[1]; ^[2]; ^[1]

Ames Lab., and Iowa State Univ., Ames, IA (United States)
National Chung Cheng Univ., Chiayi (Taiwan)

Schloegl's second model (also known as the quadratic contact process) on a lattice involves spontaneous particle annihilation at rate p and autocatalytic particle creation at empty sites with n ≥ 2 occupied neighbors. The particle creation rate for exactly n occupied neighbors is selected here as n(n - 1)/[z(z - 1)] for lattice coordination number z. We analyze this model on a Bethe lattice. Precise behavior for stochastic models on regular periodic infinite lattices is usually surmised from kinetic Monte Carlo simulation on a finite lattice with periodic boundary conditions. However, the persistence of boundary effects for a Bethe lattice complicates this process, e.g., by inducing spatially heterogenous states. This motivates the exploration of various boundary conditions and unconventional simulation ensembles on the Bethe lattice to predict behavior for infinite size. Here, we focus on z = 3, and predict a discontinuous transition to the vacuum state on the infinite lattice when p exceeds a threshold value of around 0.053.

View Accepted Manuscript (DOE)

Research Organization:: Ames Laboratory (AMES), Ames, IA (United States)

Sponsoring Organization:: Ministry of Science and Technology (MOST) of Taiwan; USDOE Office of Science (SC), Basic Energy Sciences (BES). Chemical Sciences, Geosciences & Biosciences Division

Grant/Contract Number:: AC02-07CH11358

OSTI ID:: 1817632

Journal Information:: Physical Review E, Journal Name: Physical Review E Journal Issue: 1 Vol. 104; ISSN 2470-0045

Publisher:: American Physical Society (APS)Copyright Statement

Country of Publication:: United States

Language:: English

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