| Abstract: |
| Initially developed as limiting objects that describe large networks, graphons laid the foundation to consider generalizations of mean-field spin models, like Ising model or XY-model. Statistical physics tells us that the thermodynamic limit is crucial to study phase transitions and other critical phenomena. For dense (and not so dense) graphs, this limit can be described with help of graphons or $L^p$-graphons. I will show how to use graphons to analyze phase transitions in XY model and its generalization with quenched disorder. Graphons provides a simple tool for derive and solve self-consistency equations by analyzing the spectrum of related functional operators. Moreover, for certain graphons, we can observe metastability or so-called transient states. To illustrate these statements, we discuss the Kuramoto model in the context of polariton arrays. |
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