On the linear increase of the flux tube thickness near the deconfinement transition

We study the flux tube thickness of a generic Lattice Gauge Theory near the deconfining phase transition. It is well known that the effective string model predicts a logarithmic increase of the flux tube thickness as a function of the interquark distance for any confining LGT at zero temperature. It is perhaps less known that this same model predicts a linear increase in the vicinity of the deconfinement transition. We present a precise derivation of this result and compare it with a set of high precision simulations in the case of the 3d gauge Ising model.