Vieira André P, Goles Eric, Herrmann Hans J
Universidade de Sao Paulo, Instituto de Fisica, Rua do Matao 1371, 05508-090 Sao Paulo, SP, Brazil.
Facultad de Ingeniería y Ciencias, Universidad Adolfo Ibáñez, Avenida Diagonal las Torres 2640, Peñalolén, Santiago, Chile.
Phys Rev E. 2021 Jan;103(1-1):012132. doi: 10.1103/PhysRevE.103.012132.
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.
我们研究了康威生命游戏的一个保守版本的动力学，在这个版本中，一个由死细胞和活细胞组成的对可以按照康威规则切换它们的状态，但只能通过交换位置，而不管它们之间的距离。我们的研究基于方格模拟以及平均场计算。随着死细胞密度的增加，我们确定了在一个非活跃相（其中动力学在有限时间后冻结）和一个活跃相（其中动力学在热力学极限下无限持续）之间的不连续相变。进一步增加死细胞的密度会使系统通过第二次转变回到非活跃相，该转变在方格上是连续的，但在平均场极限下是不连续的。
