Levy-driven temporally quenched dynamic critical behavior in directed percolation

Abstract: Quenched disorder in absorbing phase transitions can disrupt the structure and symmetry of reaction-diffusion processes, affecting their phase transition characteristics and offering a more accurate mapping to real physical systems. In the directed percolation (DP) universality class, time quenching is implemented through the dynamic setting of transition probabilities. We developed a non-uniform distribution time quenching method in the (1+1)-dimensional DP model, where the random quenching follows a L\'evy distribution. We use Monte Carlo (MC) simulations to study its phase structure and universality class. The critical point measurements show that this model has a critical region controlling the transition between the absorbing and active states, which changes as the parameter $ \beta $, influencing the distribution properties varies. Guided by dynamic scaling laws, we measured the continuous variation of critical exponents: particle density decay exponent $\alpha$, total particle number change exponent $ \theta $, and dynamic exponent $z$. This evidence establishes that the universality class of L\'evy-quenched DP systems evolves with distribution properties. The L\'evy-distributed quenching mechanism we introduced has broad potential applications in the theory and experiments of various absorbing phase transitions.