Critical variables of the spin model on the complete graph in the presence of antiferromagnetic interaction

We studied the spin system on the complete graph consisting of two interacting subensembles. The spins that belong to the same ensemble have ferromagnetic interactions; the inter-ensemble interactions are antiferromagnetic. We introduced the “balanced system” term, which defines the equality of the number of the nearest neighbors for spins of different sub-ensembles. It is shown that the critical variables and the scaling function are different from the classical ones of the unbalanced system. These results are confirmed by the Monte-Carlo simulation of the 3D layered spin model for both balanced and unbalanced systems.