The Kosterlitz-Thouless transition bypasses the Mermin-Wagner theorem's restriction on continuous symmetry breaking in low dimensions by operating through the unbinding of topological vortex-antivortex pairs rather than standard long-range order formation.
The provided papers (specifically papers 3 and 5) substantiate the claim that low-dimensional systems which would typically be forbidden from undergoing conventional continuous symmetry breaking due to the Mermin-Wagner theorem instead host topological phase transitions governed by vortex-antivortex unbinding, such as the BKT transition.