Critical dynamics and global persistence in a probabilistic three-states cellular automaton

TL;DR

This paper investigates the critical dynamics of a probabilistic three-states cellular automaton related to biological immune systems, focusing on dynamic critical and global persistence exponents using novel techniques.

Contribution

It introduces a new method to compute the dynamic critical exponent and applies two approaches to determine the global persistence exponent in the model.

Findings

Calculated the dynamic critical exponent $z$ using a recent technique.

Determined the global persistence exponent $ heta_{g}$ with two different methods.

Provides insights into the critical behavior of biological immune system models.

Abstract

In this work a three-states cellular automaton proposed to describe part of a biological immune system is revisited. We obtain the dynamic critical exponent $z$ of the model by means of a recent technique that mixes different initial conditions. Moreover, by using two distinct approaches, we have also calculated the global persistence exponent $\theta_{g}$, related to the probability that the order parameter of the model does not change its sign up to time $t$ [$P(t)\propto t^{-\theta_{g}}$].