DILUTE ANTIFERROMAGNETISM AND RANDOM-FIELDS IN 2-DIMENSIONAL ISING SYSTEMS

We study the two-dimensional (2D) diluted antiferromagnet in a uniform magnetic field using the real-space renormalization group in a hierarchical cell. We follow separately the probability distributions of random-exchange couplings and of magnetic fields along the renormalization process. Due to the random couplings, the initial uniform magnetic field becomes a random variable with a mean value that continuously decreases to zero. In this 2D case the flow of the probability distributions is always toward the attractor of the paramagnetic phase characterized by <T/J> = infinity and <(h/T)2> = infinity in agreement with d(c) = 2. We discuss the connections of our results with those obtained previously for the random-field problem.