The lace expansion for $\phi^{4}$

The lace expansion for $\phi^{4}$

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David Brydges, University of British Columbia
Jadwin Hall 343

The lace expansion provides a formula for the two point function which has been useful for critical percolation, self-avoiding walk and related problems in high dimensions. Recently Akira Sakai has shown that the Ising model and the one component $\phi^4$ model admit similar formulas.  I will review the basic features of the lace expansion and describe recent work with Mark Holmes and Tyler Helmuth which extends the lace expansion to O(2) symmetric $\phi^4$.