Critical behavior in random-spin systems with long-range interactions

Effects of the potential range of the interaction to critical behaviors of quenched random-spin systems are investigated in the limit M → 0 of the MN-component models by means of the renormalization-group theories. As static critical phenomena the stability of the fixed points is investigated and the critical exponents (η, γ, α, crossover index) and the equation of state are derived. These phenomena are different from those in pure systems, for the positive specific heat exponent α of the pure Heisenberg system.