On the criticality of a disordered ferromagnets’ model at 3D lattices with low coordination number

We investigate the criticality of the athermal, nonequilibrium random field Ising model on three-dimensional lattices with coordination number z=3. Using state-of-the-art numerical simulations and finite-size scaling analysis, we address a longstanding theoretical question: the absence of disorder-induced critical behavior in systems with low coordination numbers. Our results provide compelling evidence that the model lacks nontrivial criticality, as indicated by the disorder dependence of the effective critical magnetic field, the average size of spanning avalanches, and the scaling collapses of avalanche parameters. Extensive simulations, including both regular lattices and systems with preset interfaces, reveal that coordination number and lattice dimensionality are the key factors governing critical behavior. These findings not only deepen our understanding of the distinctions between nonequilibrium and equilibrium critical phenomena in disordered systems but also offer insights relevant to the design of self-assembled materials with unique structural properties.