Minimal string theory is logarithmic

We study the simplest examples of minimal string theory whose worldsheet description is the unitary (p,q) minimal model coupled to two-dimensional gravity ( Liouville field theory). In the Liouville sector, we show that four-point correlation functions of 'tachyons' exhibit logarithmic singularities, and that the theory turns out to be logarithmic. The relation with Zamolodchikov's logarithmic degenerate fields is also discussed. Our result holds for generic values of (p,q).