GFF Convergence and Six Vertex Models: Phase Transitions

This lecture discusses the convergence of Gaussian Free Fields (GFF) and the behavior of six vertex models in relation to phase transitions. The instructor begins by outlining the conditions under which the height function is delocalized, particularly focusing on the parameter C and its implications for variance in the height function. The discussion transitions to the six vertex model on a torus, emphasizing the importance of the ice rule and the conservation of arrows. The instructor explains the relationship between the six vertex model and FK percolation, detailing how configurations can be transformed and the significance of weights in these models. The lecture also covers the Bethe ansatz and its application in estimating eigenvalues of the transfer matrix, which is crucial for understanding the free energy associated with different slopes in the model. The instructor concludes by addressing the implications of these findings for continuous and discontinuous phase transitions, highlighting the ongoing research in this area.