Lower critical dimension of the random-field ising model: A Monte Carlo study

This paper presents extensive Monte Carlo simulations of the random-field Ising model in various dimensions for long times in moderately large systems, and specifically addresses the question of whether the lower critical dimension is 2 or 3. The authors find long-range order for d=3 and no long-range order for d=2. The marginality of the d=2 case is further checked by studying a system in d=ln8ln31.89 dimensions simulated by a fractal; the authors thus conclude that the lower critical dimension is 2.