Emergent Competition Between Dynamical Channels in Nonequilibrium Systems

Abstract

We introduce a rejection-free continuous-time kinetic Monte Carlo framework to study stochastic systems governed by multiple concurrent dynamical mechanisms. In this approach, the relative activity of each dynamical channel emerges self-consistently from the instantaneous configuration through its transition rates. As an illustration, we investigate a driven antiferromagnetic Ising model on a square lattice combining conservative Katz-Lebowitz-Spohn exchanges and nonconserving Glauber single-spin flips. We show that the coexistence of these dynamics qualitatively reshapes the nonequilibrium phase diagram in the temperature-field plane, stabilizing antiferromagnetic order in regions where the driving field would otherwise destroy it. Near the zero-temperature limit, the phase boundary follows a power-law scaling $T\sim|E-E_c|$ with an exponent close to unity. At intermediate temperatures, the transition belongs to the two-dimensional Ising universality class, while at low temperatures it remains continuous, with the order-parameter exponent approaching zero. Our results demonstrate that allowing competing dynamical channels to coevolve with the system can fundamentally alter its critical properties, revealing collective behavior hidden in single-dynamics descriptions.

Figures (7)

• Figure 1: (Color online) Schematic illustration of a system under the influence of two competing dynamical mechanisms. The conservative channel (two-spin exchange) has transition rate $w_{ij}$, which depends on the external parameters drive $E$ and temperature $T$, as well as on the internal energy variation $\Delta\mathcal{H}_{ij}$, and acts with probability $q_K = 1 - q_G$ determined by the instantaneous configuration. In contrast, the nonconserving channel (single-spin flip) has transition rate $w_i$, which depends on $T$ and on the internal energy variation $\Delta\mathcal{H}_{i}$, and acts with probability $q_G$, also determined by the current state of the system.
• Figure 2: (Color online) Phase diagram of the antiferromagnetic Ising model under competing dynamics between thermal relaxation via single-spin flips and driven diffusion induced by two-spin exchange (KLS) dynamics. The inset shows a logarithmic representation of the phase boundary, plotting $T$ as a function of $|E-E_c|$ with $E_c=8$. The linear behavior indicates a power-law scaling near the critical field in the limit $T\to0$, with exponent $z=1.001\pm0.001$. The fitted relation is displayed at the top of the panel. Error bars are smaller than the symbol size, and the lines are guides to the eye.
• Figure 3: (Color online) Comparison between the different critical regimes observed in the system through the analysis of $m_L^{AF}$ and the Binder cumulant $U_L$. Panels (a) and (b) show $U_L$ and $m_L^{AF}$ at $T = 0.001$ as functions of $E$, respectively, while panels (c) and (d) present $U_L$ and $m_L^{AF}$ at $T = 1$. In all panels, results are shown for different system sizes, as shown in panel (a). The vertical black dotted lines indicate the critical point of the phase transition listed in Table \ref{['Tab.1']}, determined from the crossing of the $U_L$ curves. Error bars are smaller than the symbol size, and the lines are guides to the eye.
• Figure 4: (Color online) Data collapse of the curves shown in Fig. \ref{['fig:2']}, yielding the scaling functions of Eqs. \ref{['eq:8a']} and \ref{['eq:8b']} using the critical exponents listed in Table \ref{['Tab.1']}. For clarity, the $m_0$ curves were normalized by $m_0 = 1.1322$ in panel (b) and $m_0 = 1.67$ in panel (d), without affecting the quality of the collapse.
• Figure 5: (Color online) Stationary values of the single-spin-flip activation rate, $q_G$, and of the magnetization current, $J_m$, as functions of $E$ for different values of $T$.