2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/217002We study the evolution of a random initial field under pure diffusion in various space dimensions. From numerical calculations we find that the persistence properties of the system show sharp transitions at critical dimensions d1 ~ 26 and d2 ~ 46. We also give refined measurements of the persistence exponents for low dimensions.4 pages, 5 figuresStatistical MechanicsHigh Energy Physics - LatticeHigh Energy Physics - TheoryCellular Automata and Lattice GasesAtomic Physicstext