Using finite-size-scaling methods, we study the quantum chain version of the spin-1-Blume-Capel model coupled to an imaginary field. The aim is to realize higher order non-unitary conformal field theories in a simple Ising-type spin model. We find that the first ground-state level crossing in the high-temperature phase leads to a second-order phase transition of the Yang-Lee universality class (central charge c=−22/5). The Yang-Lee transition region ends at a line of a new type of tricriticality, where the {\em three} lowest energy levels become degenerate. The analysis of the spectrum at two points on this line gives good evidence that this line belongs to the universality class of the M2,7-conformal theory with c=−68/7.
@article{arxiv.hep-th/9402143,
title = {Non-hermitian tricriticality in the Blume-Capel model with imaginary field},
author = {G. von Gehlen},
journal= {arXiv preprint arXiv:hep-th/9402143},
year = {2009}
}