Theory of phase transitions in diluted systems with competing interactions

Abstract

As a simple model of a diluted system with competing interactions, we first consider an Ising spin system on the square lattice with nearest-neighbour interaction J₁ positive, next-nearest-neighbour interaction J₂ negative, and where a fraction 1 –x of the spins is removed at random. Systematic expansions in x or 1 –x as well as Monte Carlo calculations are used to investigate the ordering of this model system. It is shown that for broad ranges of x and J₂/J₁ a spin-glass phase occurs, which consists of (anti-) ferromagnetic clusters coupled together by partially „frustrated“ bond, giving rise to a high ground-state degeneracy. Then we briefly discuss various analytical methods which can be used to calculate spin-glass properties, and compare them with our numerical results. Also other related models are mentioned. Finally we discuss to what extent these models can be applied to randomly mixed molecular crystals.