Phase transitions in a conservative game of life

André P. Vieira, Eric Goles, and Hans J. Herrmann
Phys. Rev. E 103, 012132 – Published 26 January 2021

Abstract

We investigate the dynamics of a conservative version of Conway's Game of Life, in which a pair consisting of a dead and a living cell can switch their states following Conway's rules but only by swapping their positions, irrespective of their mutual distance. Our study is based on square-lattice simulations as well as a mean-field calculation. As the density of dead cells is increased, we identify a discontinuous phase transition between an inactive phase, in which the dynamics freezes after a finite time, and an active phase, in which the dynamics persists indefinitely in the thermodynamic limit. Further increasing the density of dead cells leads the system back to an inactive phase via a second transition, which is continuous on the square lattice but discontinuous in the mean-field limit.

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  • Received 22 January 2020
  • Revised 9 January 2021
  • Accepted 12 January 2021

DOI:https://doi.org/10.1103/PhysRevE.103.012132

©2021 American Physical Society

Physics Subject Headings (PhySH)

Statistical Physics & Thermodynamics

Authors & Affiliations

André P. Vieira1, Eric Goles2, and Hans J. Herrmann3,4

  • 1Universidade de Sao Paulo, Instituto de Fisica, Rua do Matao 1371, 05508-090 Sao Paulo, SP, Brazil
  • 2Facultad de Ingeniería y Ciencias, Universidad Adolfo Ibáñez, Avenida Diagonal las Torres 2640, Peñalolén, Santiago, Chile
  • 3Departamento de Física, Universidade Federal do Ceará, 60451-970 Fortaleza, CE, Brazil
  • 4ESPCI, CNRS UMR 7636 - Laboratoire PMMH, 75005 Paris, France

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Issue

Vol. 103, Iss. 1 — January 2021

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