Subcritical two-point functions for high-dimensional statistical mechanical models

The subcritical two-point function for the Ising model, percolation, or the self-avoiding walk on Zd, decays like its critical counterpart when x is small, and exhibits the Ornstein--Zernike decay when x is large. We report recent progress on the slightly subcritical two-point function for the high-dimensional self-avoiding walk, where we obtained asymptotics that are uniform in the distance to criticality. In particular, our result reduces to the two regimes of decay, and we identify the order of the constant in the Ornstein--Zernike decay. This is based on an ongoing work with Gordon Slade.