Ising Spectroscopy II: Particles and poles at T>Tc

Abstract

I discuss particle content of the Ising field theory (the scaling limit of the Ising model in a magnetic field), in particular the evolution of its mass spectrum under the change of the scaling parameter. I consider both real and pure imaginary magnetic field. Here I address the high-temperature regime, where the spectrum of stable particles is relatively simple (there are from one to three particles, depending on the parameter). My goal is to understand analytic continuations of the masses to the domain of the parameter where they no longer exist as the stable particles. I use the natural tool -- the $2\to 2$ elastic scattering amplitude, with its poles associated with the stable particles, virtual and resonance states in a standard manner. Concentrating attention on the "real" poles (those corresponding to stable and virtual states) I propose a scenario on how the pattern of the poles evolves from the integrable point $T=T_c,\ H\neq 0$ to the free particle point $T>T_c,\ H=0$, and then, along the pure imaginary $H$, to the Yang-Lee critical point. Waypoints along this evolution path are located using TFFSA data. I also speculate about likely behavior of some of the resonance poles.