PT breaking and RG flows between multicritical Yang-Lee fixed points

We study a novel class of Renormalization Group flows which connect multicritical versions of the two-dimensional Yang-Lee edge singularity described by the conformal minimal models M(2,2n+3). The absence in these models of an order parameter implies that the flows towards and between Lee-Yang edge singularities are all related to the spontaneous breaking of PT symmetry and comprise a pattern of flows in the space of PT symmetric theories consistent with the c-theorem and the counting of relevant directions. Additionally, we find that while in a part of the phase diagram the domains of unbroken and broken PT symmetry are separated by critical manifolds of class M(2,2n+3), other parts of the boundary between the two domains are not critical.