On the basis of the theory of phase transitions, a model describing anomalies of sound attenuation coefficient close to the antiferromagnet-paramagnet phase transition in magnetic field was developed. The scaling behaviour of the sound velocity and attenuation coefficient was determined. The physical origin of the two-peak structure in the field dependent ultrasound attenuation observed in a number of antiferromagnets was identified. The theoretical results were compared with experimental results obtained for terbium.
Thermodynamics of one-dimensional finite-ranged Ising model with quenched disorder introduced by random admixture of bonds with second neighbours by means of transfer-matrix method was determined. The influence of frustrations and competition on the internal energy, specific heat, correlations functions, and susceptibility was studied.
We investigated a ±J Ising model on an infinite strip of squares of the width of one and two bonds with a random distribution of ferro- and antiferromagnetic exchange interactions. The exact ground-state energy as a function of the concentration of antiferromagnetic bonds was derived and its singular points in the complex-plane were found.