LAUSR

We consider the planar Ising model in a finite square box and we replace the temperature parameter with a function depending on the magnetization. This creates a feedback from the spin configuration onto the parameter, which drives the system towards the critical point. Using the finite-size scaling results of Cerf and Messikh (Theory Relat Fields 150(1–2):193–217, 2011. https://doi.org/10.1007/s00440-010-0272-0 ), we show that, when the size of the box grows to infinity, the temperature concentrates around the critical temperature of the planar Ising model on the square lattice.