Modified spin-wave study of random antiferromagnetic-ferromagnetic spin   chains
  We study the thermodynamics of one-dimensional quantum spin-1/2 Heisenberg ferromagnetic system with random antiferromagnetic impurity bonds. In the dilute impurity limit, we generalize the modified spin-wave theory for random spin chains, where local chemical potentials for spin-waves in ferromagnetic spin segments are introduced to ensure zero magnetization at finite temperature. This approach successfully describes the crossover from behavior of pure one-dimensional ferromagnet at high temperatures to a distinct Curie behavior due to randomness at low temperatures. We discuss the effects of impurity bond strength and concentration on the crossover and low temperature behavior. 
Xin Wan, Kun Yang, and R. N. Bhatt