全局耦合Stratonovich模型有限阵列中的非平衡相变：强耦合极限
Nonequilibrium phase transitions in finite arrays of globally coupled Stratonovich models: Strong coupling limit
摘要：
有限阵列的$N$全球耦合Stratonovich模型表现出连续的非平衡相变。在强耦合极限下，质心和相对坐标的时间尺度明显分离。后者非常快地松弛到零，并且阵列表现为由质心坐标描述的单个实体。我们用解析方法计算了稳态概率和质心坐标的矩。确定了控制参数$a_c(N)$临界值附近力矩的标度行为。我们确定了从线性到平方根缩放的交叉，随着与$a_c$距离的增加。交叉点接近$a_c$的限制$N \to \infty$再现以前的结果为无限阵列。结果得到的福克-普朗克和朗之万方法，并证实了数值模拟。对于一般的一类模型，我们表明，在参数空间中的过渡流形依赖于$N$，并确定了随机流的不动点附近的标度行为。
英文摘要：
A finite array of $N$ globally coupled Stratonovich models exhibits a continuous nonequilibrium phase transition. In the limit of strong coupling there is a clear separation of time scales of center of mass and relative coordinates. The latter relax very fast to zero and the array behaves as a single entity described by the center of mass coordinate. We compute analytically the stationary probability and the moments of the center of mass coordinate. The scaling behaviour of the moments near the critical value of the control parameter $a_c(N)$ is determined. We identify a crossover from linear to square root scaling with increasing distance from $a_c$. The crossover point approaches $a_c$ in the limit $N \to \infty$ which reproduces previous results for infinite arrays. The results are obtained in both the Fokker-Planck and the Langevin approach and are corroborated by numerical simulations. For a general class of models we show that the transition manifold in the parameter space depends on $N$ and is determined by the scaling behaviour near a fixed point of the stochastic flow.
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