Phase Transitions in a Non-equilibrium System with Parity Conservation and Long-range Diffusion

The Contact process is the simplest model for phase transitions out-equilibrium and it was originally introduced to describe epidemic spreading models. In the present work, we study the effect of long-range interactions promoted by Levy flights in an out-equilibrium system in which the parity is conserved. This model is of great interest to the scientific community working in phase transitions and critical phenomena, since it is expected to present a universality class that differs from that common Directed Percolation - DP. We investigate the critical properties of this system using computational techniques and finite-size scaling. Through the Monte Carlo simulation method, we analyzed the region of transition on linear finite lattices with an odd number of sites and initially totally occupied. We estimate the critical point $p_c$ through the scale invariance of the particles density cumulant. After finding $p_c$, it was possible to determine the set of critical exponents that characterize the universal behavior in the neighborhood of the second order phase transition. From such analysis, we found a set of exponents in agreement with the already presented in the literature, besides new critical quantities which have not been studied previously for systems with parity conservation and long range diffusion. Our results confirm that the present model depicts a non-equilibrium phase transition that don't belong to the DP's universality class. Therefore, we can assert that a new set of critical exponents arises from the effects of parity conservation and long-range interactions. Further, we unveil that the critical order parameter distribution evolves from the Gaussian to exponential form as the diffusion process becomes of longer range.