Ising model at zero temperature leads to a ferromagnetic state asymptotically. There are two such possible states linked by symmetry, and Glauber–Ising dynamics are employed to reach them. In some stochastic or deterministic dynamical systems, the same absorbing state with 𝒵2 symmetry is reached. This transition often belongs to the directed Ising (DI) class where dynamic exponents and persistence exponent are different. In asymmetrically coupled sequentially updated logistic maps, the transition belongs to the DI class. We study changes in the nature of transition with an update scheme. Even with the synchronous update, the transition still belongs to the DI class. We also study a synchronous probabilistic update scheme in which each site is updated with the probability p. The order parameter decays with an exponent 0.5 in this scheme. Nevertheless, the dynamic exponent z is less than 2 even for small values of p indicating a very slow crossover to the Ising class. However, with a random asynchronous update, we recover z = 2. In the presence of feedback, synchronous update leads to a transition in the DI universality class which changes to Ising class for synchronous probabilistic update.

中文翻译：

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更新模式对耦合 Logistic 映射普遍性类的影响：将 Ising 定向到 Ising 类

零温度下的伊辛模型渐近地导致铁磁状态。有两种这样的可能状态通过对称性联系起来，并且使用 Glauber-Ising 动力学来达到它们。在一些随机或确定性动力系统中，相同的吸收状态与𝒵2达到对称。这种转变通常属于动态指数和持久指数不同的有向伊辛 (DI) 类。在不对称耦合的顺序更新逻辑图中，转换属于 DI 类。我们使用更新方案研究过渡性质的变化。即使是同步更新，transition 仍然属于 DI 类。我们还研究了一种同步概率更新方案，其中每个站点都以概率更新p. 阶参数随指数衰减0.5在这个方案中。然而，动态指数z小于2即使对于小的值p表明与 Ising 类的交叉非常缓慢。然而，通过随机异步更新，我们恢复z = 2. 在存在反馈的情况下，同步更新会导致 DI 通用类中的转换，该类变为 Ising 类以进行同步概率更新。