Renormalization group for an Ising system with competing interactions

Overview & Synopsis

We apply a Position Space Renormalization Group approach to the Ising Hamiltonian in a square lattice with first (J1) and second (J 2) neighbour exchange interactions. The full phase diagram is obtained with three distinct ordered phases : ferro (F), antiferro (AF) and superantiferromagnetic (SAF). In particular, in the last one, the competing interactions J 1 and J2 < 0, play a crucial role yielding a two-fold space degeneracy of the ground states. This behaviour is reproduced in the present approach by a bifurcated two-fold attractor for this phase. Moreover, the non-universal character of the SAF - P transition is inferred from the Renormalization Group trajectories near the critical line.