Random antiphase state and frustration in two dimensions

Abstract
The phase diagram of the frustration model of random interactions ± J between nearest neighbour Ising spins on a square lattice is studied in the (T, x) plane : T temperature, x concentration of antiferromagnetic interactions. At T = 0 K exact ground states are generated by a new algorithm of graph theory and maps of rigid bonds or solidary spins for all ground states are obtained. At intermediate x it is found a new phase made up of erratic magnetic walls (lines). At T ≠ 0 K a simple renormalization group approach confirms the existence of the random antiphase state