Ginzburg-Landau description for multicritical Yang-Lee models

We revisit and extend Fisher’s argument for a Ginzburg-Landau description of multicritical Yang-Lee models in terms of a single boson Lagrangian with potential φ²(iφ)ⁿ. We explicitly study the cases of n = 1, 2 by a Truncated Hamiltonian Approach based on the free massive boson perturbed by PT symmetric deformations, providing clear evidence of the spontaneous breaking of PT symmetry. For n = 1, the symmetric and the broken phases are separated by the critical point corresponding to the minimal model $\mathcal{M}\left(2,5\right)$ \( \mathcal{M}\left(2,5\right) \) , while for n = 2, they are separated by a critical manifold corresponding to the minimal model $\mathcal{M}\left(2,5\right)$ \( \mathcal{M}\left(2,5\right) \) with $\mathcal{M}\left(2,7\right)$ \( \mathcal{M}\left(2,7\right) \) on its boundary. Our numerical analysis strongly supports our Ginzburg-Landau descriptions for multicritical Yang-Lee models.