Um Jaegon, Hong Hyunsuk, Park Hyunggyu
Department of Physics, Pohang University of Science and Technology, Pohang, 37673, South Korea.
Department of Physics and Research Institute of Physics and Chemistry, Jeonbuk National University, Jeonju, 54896, South Korea.
Sci Rep. 2024 Mar 21;14(1):6816. doi: 10.1038/s41598-024-57323-4.
This study investigates the suitability of the annealed approximation in high-dimensional systems characterized by dense networks with quenched link disorder, employing models of coupled oscillators. We demonstrate that dynamic equations governing dense-network systems converge to those of the complete-graph version in the thermodynamic limit, where link disorder fluctuations vanish entirely. Consequently, the annealed-network systems, where fluctuations are attenuated, also exhibit the same dynamic behavior in the thermodynamic limit. However, a significant discrepancy arises in the incoherent (disordered) phase wherein the finite-size behavior becomes critical in determining the steady-state pattern. To explicitly elucidate this discrepancy, we focus on identical oscillators subject to competitive attractive and repulsive couplings. In the incoherent phase of dense networks, we observe the manifestation of random irregular states. In contrast, the annealed approximation yields a symmetric (regular) incoherent state where two oppositely coherent clusters of oscillators coexist, accompanied by the vanishing order parameter. Our findings imply that the annealed approximation should be employed with caution even in dense-network systems, particularly in the disordered phase.
本研究利用耦合振子模型，研究了在具有淬火链路无序的密集网络所表征的高维系统中退火近似的适用性。我们证明，在热力学极限下，控制密集网络系统的动力学方程收敛于完全图版本的方程，此时链路无序涨落完全消失。因此，涨落被衰减的退火网络系统在热力学极限下也表现出相同的动力学行为。然而，在非相干（无序）相中出现了显著差异，其中有限尺寸行为在确定稳态模式时变得至关重要。为了明确阐明这种差异，我们关注受到竞争性吸引和排斥耦合的相同振子。在密集网络的非相干相中，我们观察到随机不规则状态的表现。相比之下，退火近似产生了一种对称（规则）的非相干状态，其中两个方向相反的相干振子簇共存，伴随着序参量的消失。我们的研究结果表明，即使在密集网络系统中，特别是在无序相中，也应谨慎使用退火近似。
