School of Physics and Materials Science, Anhui University, Hefei 230601, China.
Department of Physics, Anqing Normal University, Anqing 246011, China.
Chaos. 2017 Aug;27(8):081102. doi: 10.1063/1.4993520.
We theoretically study noise-induced phase switch phenomena in an inertial majority-vote (IMV) model introduced in a recent paper [Chen et al., Phys. Rev. E 95, 042304 (2017)]. The IMV model generates a strong hysteresis behavior as the noise intensity f goes forward and backward, a main characteristic of a first-order phase transition, in contrast to a second-order phase transition in the original MV model. Using the Wentzel-Kramers-Brillouin approximation for the master equation, we reduce the problem to finding the zero-energy trajectories in an effective Hamiltonian system, and the mean switching time depends exponentially on the associated action and the number of particles N. Within the hysteresis region, we find that the actions, along the optimal forward switching path from the ordered phase (OP) to disordered phase (DP) and its backward path show distinct variation trends with f, and intersect at f = f that determines the coexisting line of the OP and DP. This results in a nonmonotonic dependence of the mean switching time between two symmetric OPs on f, with a minimum at f for sufficiently large N. Finally, the theoretical results are validated by Monte Carlo simulations.
我们从理论上研究了最近一篇论文中引入的惯性多数表决（IMV）模型中的噪声诱导的相开关现象[Chen 等人，Phys. Rev. E 95, 042304 (2017)]。与原始 MV 模型中的二阶相变相比，IMV 模型作为噪声强度 f 的前进和后退，会产生强烈的滞后行为，这是一阶相变的主要特征。我们使用主方程的 Wentzel-Kramers-Brillouin 近似，将问题简化为在有效哈密顿系统中寻找零能轨迹，并且平均切换时间与相关的作用量和粒子数 N 呈指数关系。在滞后区域中，我们发现沿着从有序相（OP）到无序相（DP）的最优正向切换路径以及其反向路径的作用量与 f 具有明显不同的变化趋势，并在 f=f 处相交，该交点确定了 OP 和 DP 的共存线。这导致在两个对称 OP 之间的平均切换时间对 f 的非单调依赖性，并且在足够大的 N 时在 f 处存在最小值。最后，通过蒙特卡罗模拟验证了理论结果。
