Double-Scaling Limit of a Broken Symmetry Quantum Field Theory

The Ising limit of a conventional Hermitian parity-symmetric scalar quantum field theory is a correlated limit in which two bare Lagrangian parameters, the coupling constant g and the negative mass squared −m2, both approach infinity with the ratio −m2/g = α > 0 held fixed. In this limit the renormalized mass of the asymptotic theory is finite. Moreover, the limiting theory exhibits universal properties. For a non-Hermitian PT -symmetric Lagrangian lacking parity symmetry, whose interaction term has the form −g(iφ)N/N , the renormalized mass diverges in this correlated limit. Nevertheless, the asymptotic theory still has interesting properties. For example, the one-point Green’s