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A<sc>bstract</sc> It has been proposed that the Ginzburg-Landau description of the non-unitary conformal minimal modelM(3, 8) is provided by the Euclidean theory of two real scalar fields with third-order interactions that have imaginary coefficients. The same lagrangian describes the non-unitary modelM(3, 10), which is a product of two Yang-Lee theoriesM(2, 5), and the Renormalization Group flow from it toM(3, 8). This proposal has recently passed an important consistency check, due to Y. Nakayama and T. Tanaka, based on the anomaly matching for non-invertible topological lines. In this paper, we elaborate the earlier proposal and argue that the two-field theory describes theDseries modular invariants of bothM(3, 8) andM(3, 10). We further propose the Ginzburg-Landau descriptions of the entire class ofDseries minimal modelsM(q, 3q– 1) andM(q, 3q+ 1), with odd integerq. They involve$$ \mathcal{PT} $$ $\mathrm{PT}$symmetric theories of two scalar fields with interactions of orderqmultiplied by imaginary coupling constants.