Disorder to Order Transition in 1D non-reciprocal Cahn-Hilliard Model

Abstract

We present the phenomenology of the one dimensional non-reciprocal Cahn Hilliard model for varying non-reciprocity $(\alpha )$ and different boundary conditions. At small $\alpha$, a perturbed uniform state evolves to a defect laden configuration that lacks global polar order. Defects are the sources and sinks of travelling waves. For a given $\alpha$, defects with a unique wave number that increases monotonically with $\alpha$ are selected. A critical threshold ${\alpha }_c$ marks the onset of a transition to states with finite global polar order. For periodic boundary conditions, above ${\alpha }_c$, the system shows travelling waves that are completely ordered. In contrast, travelling waves are incompatible with the Neumann and Dirichlet boundary conditions. Instead, for $\alpha \gtrsim {\alpha }_c$, we find fluctuating domains that show intermittent polar order and at large $\alpha$, the system partitions into two domains with opposite polar order.

9 pages and 8 figures