Spectral dimension determines criticality in nonreciprocal phase oscillators (opens in new tab)

Spectral dimension is a key determinant of critical phenomena, but its role in nonreciprocal systems remains unexplored. We study noisy identical Kuramoto-Sakaguchi oscillators with phase lag $\alpha \in [0,\pi/2)$, where $\alpha>0$ induces nonreciprocal interactions. Numerical phase diagrams in the $(d_s,\alpha)$ plane in complex networks, where $d_s$ denotes the spectral dimension, reveal a critical phase lag $\alpha_c$, below which spontane...