Title: Distribution of the magnetization of the critical Ising model on sparse random graphs
Abstract: We study the Ising model on random d-regular and sparse Erdos-Renyi graphs at the critical temperature, focusing on the asymptotic distribution of the sum of spins, called the magnetization of the model. In the random regular case, the analysis uses the Small Subgraph Conditioning Method, which has been the standard approach in similar problems. In the Erdos-Renyi case, however, we need to explain additional fluctuations that show up in the partition function, leading to a phenomenon that, to our knowledge, has not been observed in other models. As a corollary, we derive lower bounds for the mixing time of the Glauber dynamics at the critical temperature for both graph models. Joint work will Allan Sly.
Reza Gheissari
Email