First-Order Phase Transitions in Memristive Networks

The development of neuromorphic systems based on memristive elements - resistors with memory - requires a fundamental understanding of their collective dynamics when organized in networks. Here, we study an experimentally inspired model of two-dimensional disordered memristive networks subject to a slowly ramped voltage and show that these networks undergo a first-order phase transition in the conductivity for sufficiently high values of memory, as quantified by the memristive ON/OFF ratio. We also provide a mean-field theory, inspired by the zero-temperature random-field Ising model, that reproduces many features of the transition. Verification of our predictions is within reach of present experimentally realizable systems.