Ginzburg-Landau description for multicritical Yang-Lee models

Abstract

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 $\ddot{I}{†}^2(i\ddot{I}†{)}^n$. We explicitly study the cases of $n=1,2$ by a Truncated Hamiltonian Approach based on the free massive boson perturbed by $\mathbf{P}\mathbf{T}$ symmetric deformations, providing clear evidence of the spontaneous breaking of $\mathbf{P}\mathbf{T}$ symmetry. For $n=1$, the symmetric and the broken phases are separated by the critical point corresponding to the minimal model $\mathcal{M}(2,5)$, while for $n=2$, they are separated by a critical manifold corresponding to the minimal model $\mathcal{M}(2,5)$ with $\mathcal{M}(2,7)$ on its boundary. Our numerical analysis strongly supports our Ginzburg-Landau descriptions for multicritical Yang-Lee models.

28 pages, 10 figures