Multicriticality in Yang-Lee edge singularity

In this paper we study the non-unitary deformations of the two-dimensional Tricritical Ising Model obtained by coupling its two spin Z(2) odd operators to imaginary magnetic fields. Varying the strengths of these imaginary magnetic fields and adjusting correspondingly the coupling constants of the two spin Z(2) even fields, we establish the presence of two universality classes of infrared fixed points on the critical surface. The first class corresponds to the familiar Yang-Lee edge singularity, while the second class to its tricritical version. We argue that these two universality classes are controlled by the confor-mal non-unitary minimal models M(2, 5) and M(2, 7) respectively, which is supported by considerations based on P T symmetry and the corresponding extension of Zamolodchikov's c-theorem, and also verified numerically using the truncated conformal space approach. Our results are in agreement with a previous numerical study of the lattice version of the Tricritical Ising Model [1]. We also conjecture the classes of universality corresponding to higher non-unitary multicritical points obtained by perturbing the conformal unitary models with imaginary coupling magnetic fields.

Automated summary

In this paper, we investigate the non-unitary deformations of the two-dimensional Tricritical Ising Model by coupling its two spin Z(2) odd operators to imaginary magnetic fields. By varying the strengths of these imaginary magnetic fields and adjusting the coupling constants of the two spin Z(2) even fields accordingly, we identify two universality classes of infrared fixed points on the critical surface. We argue that these classes are controlled by the non-unitary minimal models M(2, 5) and M(2, 7) respectively, supported by considerations based on PT symmetry and the extension of Zamolodchikov's c-theorem, and verified numerically using the truncated conformal space approach. Our results are consistent with a previous numerical study of the lattice version of the Tricritical Ising Model [1]. We also conjecture the universality classes corresponding to higher non-unitary multicritical points obtained by perturbing the conformal unitary models with imaginary coupling magnetic fields.