Griffiths-Hurst-Sherman Inequalities and a Lee-Yang Therorem for the(ϕ4)2Field Theory

Abstract

The Griffiths-Hurst-Sherman inequalities and the Lee-Yang zero theorem in the theory of Ising ferromagnets are shown to hold in a two-dimensional self-coupled Bose quantume field theory with interaction: $a{\ensuremath{\phi}}^{4}+b{\ensuremath{\phi}}^{2}\ensuremath{-}\ensuremath{\mu}\ensuremath{\phi}$:. Applications include the continuity of the infinite-volume "magnetization," $〈\ensuremath{\phi}(0)〉$, away from $\ensuremath{\mu}=0$. Our results should carry over to three or four dimensions once it is known how to control the ultraviolet divergences in these theories.