具有加性噪声的全局耦合势系统中的不连续跃迁
Discontinuous transitions in globally coupled potential systems with additive noise
摘要：
研究了在加性高斯白噪声作用下，在具有$n$阶饱和项的双势阱中运动的全局耦合过阻尼组元的无限阵列.该系统表现出一个连续的相变从对称相到一个破缺相。定性行为与$n$无关。计算强噪声和弱噪声的临界点，这些极限也是临界点的界限。引入一个额外的非线性，使潜力可以有三个最小值，导致更丰富的行为。在那里的参数空间分为三个区域，一个区域的对称相，一个区域的对称性破缺相和一个区域，两个阶段共存。共存区域通过不连续的相变坍缩成另一个，而对称相和对称性破缺相之间的过渡是连续的。三个区域相交处的三临界点可以针对强噪声和弱噪声来计算。这些极限值形成了三临界点的最优边界。在该区域的共存模拟有限系统进行。人们发现有限大系统的平稳分布与无限大系统的平稳分布有质的不同。因此，平稳性和大系统尺寸的限制并不互换。
英文摘要：
An infinite array of globally coupled overdamped constituents moving in a double-well potential with $n$-th order saturation term under the influence of additive Gaussian white noise is investigated. The system exhibits a continuous phase transition from a symmetric phase to a symmetry-broken phase. The qualitative behavior is independent on $n$. The critical point is calculated for strong and for weak noise, these limits are also bounds for the critical point. Introducing an additional nonlinearity, such that the potential can have up to three minima, leads to richer behavior. There the parameter space divides in three regions, a region with a symmetric phase, a region with a phase of broken symmetry and a region where both phases coexist. The region of coexistence collapses into one of the others via a discontinuous phase transition whereas the transition between the symmetric phase and the phase of broken symmetry is continuous. The tricritical point where the three regions intersect, can be calculated for strong and for weak noise. These limiting values form optimal bounds on the tricritical point. In the region of coexistence simulations of finite systems are performed. One finds that the stationary distribution of finite but large systems differs qualitatively from the one of the infinite system. Hence the limits of stationarity and large system size do not commute.
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