Emmanuel Michta, Gordon Slade: Finite-size scaling and the self-avoiding walk


How long does a self-avoiding walk on a finite transitive > graph have to be before it `feels’ the effect of the finite volume? We > discuss the elementary exact solution for self-avoiding walk on the > complete graph, which shows a separation into a dilute phase, a critical > window, and a dense phase.  The exact solution on the complete graph > provides a prototype for self-avoiding walk on other high-dimensional > finite transitive graphs, including the hypercube and discrete tori in > dimensions d > 4, and we discuss recent results for the dilute phase > obtained in these two settings via the lace expansion. Related work in > progress with Jiwoon Park (University of Cambridge) on the finite-size > scaling of the 4-dimensional hierarchical n-component |\phi|^4 > spin model will also be mentioned.


Based on 




Password Protected

This video is password-protected. Please verify with a password to unlock the content.