EXACT MAGNETIC TRANSITIONS IN THE UNION JACK MODEL

Abstract

We present the exact expression for the partition function per spin in the thermodynamic limit, for the general "union jack" model. In effect, in this model we treat nearest and next nearest neighbors interactions. For the particular case in which the interaction parameters within the unit cell have the values e, = e2, e3 = ae4, e5 = Ne3 and e6 = Ne4 with a = +/-1 and N any real number, we present explicit phase diagrams and rigorous exact expressions for the loci of the transitions. These diagrams split up in several regions which we are able to characterize by their magnetic configurations. We do that by calculating the exact correlation functions between the spins in the unit cell.