We propose three different lattice operators to measure the intrinsic width xi_I of the chromoelectric flux tube in pure lattice gauge theories. In order to test these proposals we evaluate them for SU(2) and Ising LGTs in (2+1) dimensions in the vic
inity of the deconfinement transition. Using dimensional reduction, we could perform the calculation in the effective 2d spin model using standard S-matrix techniques. We consistently found the same result for the three lattice operators. This result can be expressed in terms of the finite temperature string tension as follows xi_I=frac{T}{2sigma(T)} and implies that the intrinsic width of the flux tube diverges as the deconfinement transition is approached.
In this contribution we review some recent results about the emergence of 2D integrable systems in 3D Lattice Gauge Theories near the deconfinement transition. We focus on some concrete examples involving the flux tube thickness, the ratio of k-strin
g tensions and Polyakov loops correlators in various models.
It was recently pointed out that simple scaling properties of Polyakov correlation functions of gauge systems in the confining phase suggest that the ratios of k-string tensions in the low temperature region is constant up to terms of order T^3. Here
we argue that, at least in a three-dimensional Z_4 gauge model, the above ratios are constant in the whole confining phase. This result is obtained by combining numerical experiments with known exact results on the mass spectrum of an integrable two-dimensional spin model describing the infrared behaviour of the gauge system near the deconfining transition.
