Order-disorder transition in an external field in random ferromagnets and nematic elastomers

We study theoretically the effect of external field on random anisotropy ferromagnets and nematic elastomers. The system evolves on increasing field from the correlated spin glass state to the aligned ferromagnetic state via a first order phase transition at a threshold field accompanied by a significant jump of the average magnetization. The mean magnetization growth is due to reorientation, rather than growth of individual domains. We discuss the additional hardening mechanisms in nematic elastomers that increase the threshold of the transition observed experimentally and lead to the ''fossil'' domain walls left in the aligned system.