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We simulate five different systems belonging to the universality class of thegauge dual of three-dimensional random percolation to study the underlyingeffective string theory at finite temperature. All the data for the finitetemperature string tension, when expressed by means of adimensional variables,are nicely described by a unique scaling function. We calculate the first fewterms of the string tension up to order $T^6$ and compare to differenttheoretical predictions. We obtain unambiguous evidence that the coefficientsof $T^2$ and $T^4$ terms coincide with those of the Nambu-Goto string, asexpected, while the $T^6$ term strongly differs and is characteristic of theuniversality class of this specific gauge theory.

The confining string beyond the free-string approximation in the gauge dual of percolation