Proof that $\delta =2$ and $\beta =1$ under the Triangle Condition

Abstract

We use the finiteness of the triangle diagram in order to establish that certain critical exponents take on their mean-field values. We again rely on the differential inequalities developed in chapter 3, and complement them with a differential inequality involving the triangle diagram. We then prove that, under the triangle condition, the critical exponents $\delta$ and $\beta$ take on their mean-field values $\delta$ = 2 and $\beta$ = 1.