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

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: $a{\varphi }^4+b{\varphi }^2-\mu \varphi$:. Applications include the continuity of the infinite-volume "magnetization," $〈\varphi \mathrm{}\left(0\right)\mathrm{}〉$, away from $\mu =0\mathrm{}$. Our results should carry over to three or four dimensions once it is known how to control the ultraviolet divergences in these theories.