LOW-ENERGY BEHAVIOR OF A RANDOM CLASSICAL HEISENBERG CHAIN

Low-energy magnons in a classical Heisenberg chain with random nearest -neighbor interactions are investigated using the negative eigenvalue counting technique. A detailed study is made for a range of concentrat ions of ''wrong sign'' bonds (i.e., c less than or equal to 0.1 and c greater than or equal to 0.9). It is found that low-energy magnons hav e an anomalous power-law (2/3) behavior in the spectrum for random sig n-fixed magnitude exchange interactions. Combining these and previous results, a phenomenological fit is established describing the concentr ation dependence of the spectrum for a wide range of values of c. A di scussion based on scaling arguments is presented to account for the an omalous power law for arbitrary concentrations. The general case where the magnitudes and the signs of the exchange interactions and the mag nitudes of the spins are all random quantities is further investigated to check whether the anomalous power-law behavior holds. For uniform (flat), nonsingular distributions of the random quantities, the 2/3 po wer in the spectrum is obtained but for singular distributions and mix ed distributions (e.g., the magnitude of the spin has a singular distr ibution while the magnitude of the exchange interaction has a regular distribution) significant deviations from the 2/3 power law occur.