Seminars & Colloquia Calendar

It would be nice one day to prove that lattice models with short-range interactions, such as the 2d or 3d Ising model, possess a renormalization-group fixed point. But it’s hard, since these fixed points are strongly coupled. The situation is better for the long-range Ising model, where the spin-spin interaction is powerlike. Tuning the power one can make the fixed point weakly coupled. Weakly coupled non-gaussian fixed points in the scalar field theory with a non-local kinetic term and a quartic interactions have been constructed 20 years ago by Brydges et al. Similar fermionic fixed points have been considered by Gawedzki and Kupiainen in mid-80’s. Recently Alessandro Giuliani, Vieri Mastropietro and myself have revisited the problem of fermionic fixed points in arXiv:2008.04361. We have proved that, at weak coupling, the fixed point is analytic in epsilon (the deviation from marginality). I will review what is known or conjectured about bosonic and fermionic long-range fixed points. In particular I will discuss the long-range to short-range crossover.