The Non-Reciprocal Ising Model with Zero, One, and Two Conservation Laws

Kristian Blom

Non-variational continuum models, such as the non-reciprocal Cahn–Hilliard and Allen–Cahn equations, are often derived from phenomenological arguments, and their consistency with underlying microscopic dynamics is not guaranteed. In this talk, we present a bottom-up construction of a non-reciprocal phase-field system, starting from two coupled Ising models with non-reciprocal interactions. These models evolve according to Kawasaki and/or Glauber dynamics, allowing us to investigate the impact of conservation laws associated with the magnetization in each lattice. Our analysis identifies the conditions under which oscillatory phases emerge and clarifies how these phases depend on both reciprocal and non-reciprocal couplings, as well as on the presence or absence of conservation laws in the respective subsystems.