Title: Phase transition of singular Gibbs measures for three-dimensional Schrödinger-wave system Show Chinese title

Title: 三维薛定谔-波系统的奇异吉布斯测度的相变

Abstract: We study singular Gibbs measures for the three-dimensional Schr\"odinger-wave system, also known as the Yukawa system. Our primary result is the phase transition between weak and strong coupling cases, a phenomenon absent in one- and two-dimensional cases. Therefore, the three-dimensional model turns out to be critical, exhibiting the phase transition. In the weak coupling case, the Gibbs measure can be normalized as a probability measure and is shown to be singular with respect to the Gaussian free field. Conversely, in the strong coupling case, the Gibbs measure cannot be constructed as a probability measure. In particular, the finite-dimensional truncated Gibbs measures have no weak limit in an appropriate space, even up to a subsequence. Show Chinese abstract

Abstract: 我们研究三维薛定谔-波系统的奇异吉布斯测度，也称为库伦系统。 我们的主要结果是弱耦合和强耦合情况之间的相变，这一现象在一维和二维情况下不存在。 因此，三维模型被证明是临界的，表现出相变。 在弱耦合情况下，吉布斯测度可以归一化为一个概率测度，并且相对于高斯自由场是奇异的。 相反，在强耦合情况下，吉布斯测度无法构造为一个概率测度。 特别是，有限维截断的吉布斯测度在适当的空间中甚至无法在子序列上存在弱极限。