Tightness of the maximum of Ginzburg-Landau fields
Tightness of the maximum of Ginzburg-Landau fields
We consider the discrete Ginzburg-Landau field with potential satisfying a uniform convexity condition, in the critical dimension $d=2$, and prove that its maximum over boxes of sidelength $N$, centered by an explicit $N$-dependent centering, is tight.