Influence of non-reciprocal interactions on classical phase transitions

Determine how non-reciprocal interactions—namely, asymmetric and state-dependent couplings that violate reciprocity (J_ij ≠ J_ji), as exemplified by Ising models with Glauber dynamics—affect classical phase transitions, including their impact on the nature of the transition (continuous versus discontinuous), critical temperatures, and critical exponents and universality classes.

Background

Non-reciprocal interactions, which break the action–reaction principle, arise widely in non-equilibrium systems across social dynamics, active matter, and non-Hermitian physics. Recent work has explored such interactions primarily in multi-species settings or vector models (e.g., XY models with vision-cone couplings), leaving foundational aspects of how non-reciprocity modifies equilibrium-like critical behavior insufficiently characterized.

This paper introduces a single-species Ising framework with state-dependent, non-reciprocal couplings and studies mean-field and two-dimensional lattice realizations. The authors find shifts in critical temperatures, the emergence of discontinuous transitions, and apparent deviations of the order-parameter exponent β from the 2D Ising universality class, highlighting that a general understanding of how non-reciprocity changes classical phase transitions is still lacking.