  We study the triangular lattice Ising model with a finite number of
vertically stacked layers and demonstrate a low temperature reentrance of two
Berezinskii-Kosterlitz-Thouless transitions, which results in an extended
disordered regime down to $T=0$. Numerical results are complemented with the
derivation of an effective low-temperature dimer theory. Contrary to order by
disorder, we present a new scenario for fluctuation-induced ordering in
frustrated spin systems. While short-range spin-spin correlations are enhanced
by fluctuations, quasi-long-range ordering is precluded at low enough
temperatures by proliferation of topological defects.
