Abstract
The problem of generating ground states of a quenched random Ising spin system with variable concentration of mixed-neighbour exchange couplings (Jij()0) on a planar lattice (frustration model) is mapped into the problem of the Chinese postman which has been solved by a polynomial algorithm known as Edmond's algorithm. This algorithm is transposed and applied to the frustration problem. Not only is one particular ground state generated, but a post-optimal algorithm is established which gives the map of the rigid bonds and solidary spins (bonds in the same state for all ground states). This study of the rigidity on a square lattice reveals three distinct regimes by varying x, the concentration of negative bonds: a low-concentration regime where the ground states are rigid and ferromagnetic; an intermediate regime 0.1<or approximately=x<or approximately=0.15 where the rigid ground states are structured in an antiphase domain separated by magnetic walls; a high-concentration regime where the clustering of solidary spins is finite and separated by fracture lines. These defects characterise the phase transitions between the ferromagnetic, the random antiphase and the paramagnetic states which occur with increasing x.