A laboratory seminar will be held on Monday, November 24th, at 6:00 PM.
Speaker: Artem Alexandrov
Title: Spin Systems and Graph Limits
Abstract: Spin models play a significant role in the study of phase transitions. An important fact is that phase transitions exist (in the strict sense of the word) only in the thermodynamic limit. For spin models on regular lattices, such a limit is relatively easy to construct, while for models on more complex graphs, construction requires effort and more sophisticated methods. Graph limits naturally arise in such a problem, and were first discussed by L. Lovasz, C. Borgs, and others in the context of extremal graph theory about 15-20 years ago. Since the limits of dense graphs have been best studied, I will primarily discuss this case. As a simple example, I will consider the Ising model and the construction of its thermodynamic limit using graphons. I'll explain how different types of convergence in graph theory relate to statistical physics, then show how graphons can be used to analyze transition states in the Ising model. If time permits, I'll briefly touch on the case of sparse graphs. This talk is based on the paper "Thermodynamic limit of spin systems on random graphs" (https://doi.org/10.1103/PhysRevResearch.6.013011) (A. Searly, J. Tindall) and our recent paper with Georgy Medvedev, arXiv:2511.10838 (https://arxiv.org/abs/2511.10838).