  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.
