Nonreciprocal Blume-Capel Model with Antisymmetric Single-Ion Anisotropies

TL;DR

This paper explores how nonreciprocal interactions and vacancy energetics influence phase transitions and order stability in a two-species Blume-Capel model, revealing novel critical phenomena and the role of defects.

Contribution

It introduces the impact of vacancy energetics on stabilizing static order and critical behaviour in nonreciprocal Blume-Capel models, combining mean-field analysis with large-scale simulations.

Findings

Vacancy energetics can restore static order in nonreciprocal systems.

Disorder to static transition in 2D is in the Ising universality class.

Defects induce novel critical phenomena and phase transition lines.

Abstract

We investigate the interplay between nonreciprocal interactions and chemical-potential imbalance in a two-species nonreciprocal Blume-Capel model. Combining a systematic mean-field bifurcation analysis with large-scale Monte Carlo simulations in two and three dimensions, we map the model's dynamical regimes and transitions. Mean-field theory predicts a rich phase structure -- disorder, a time-dependent 'swap' (limit-cycle) phase, and static ordered states -- separated by Hopf, saddle-node on invariant circle, saddle-node of limit cycles, pitchfork and saddle-node bifurcations. In two dimensions, Monte Carlo simulations reveal that spiral defects destabilise global swapping and, unless vacancies are strongly favoured, destroy long-range order. Crucially, a finite single-ion anisotropy $\Delta_\alpha = - \Delta_\beta$ promotes vacancy occupation in the $\alpha$ species and suppresses nonreciprocal dynamics, thereby restoring a robust static ordered phase. Finite-size scaling of susceptibility and Binder cumulants places the disorder to static transition firmly in the 2D Ising universality class. Moreover, within the static ordered phase, we observe a crossover that sharpens into a line of first-order phase transitions; these two regimes are separated by a critical point, analogous to the termination of the liquid-gas coexistence curve. In three dimensions, simulations largely mirror mean-field expectations, though swap to static ordering occurs indirectly via a disordered regime. Our results demonstrate that vacancy energetics provide a simple, experimentally relevant control knob that stabilises equilibrium-like order in nonreciprocal systems and that defects can generate novel critical behaviour.