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arXiv · 2306.17013

Phase transition of singular Gibbs measures for three-dimensional Schr\"odinger-wave system

Kihoon Seong
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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.

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Kihoon Seong. 2023-06-29. Phase transition of singular Gibbs measures for three-dimensional Schr\"odinger-wave system. https://arxiv.org/abs/2306.17013

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