We use the zero-temperature random-field Ising model to study hysteretic behavior at first-order phase transitions. Sweeping the external field through zero, the model exhibits hysteresis, the return-point memory effect, and avalanche fluctuations.There is a critical value of disorder at which a jump in the magnetization (corresponding to an infinite avalanche) first occurs. We study the universal behavior at this critical point using mean-field theory, and also present preliminary results of numerical simulations in three dimensions.

No abstract

No abstract

A variety of phonon-gas phenomena in nonmetals are discussed in a unified manner using a set of macroscopic equations developed from the solution of the linearized phonon Boltzmann equation. This set of macroscopic equations, appropriate for the description of a low-temperature phonon gas, is solved for a cylindrical sample in the limit ) z(&R; ) &)~*))R'. Here X& is the normal-process mean free path, Xz' is the mean free path for momentum-loss scattering calculated in the Ziman limit, and R is the radius of the sample. The solution in this limit exhibits Poiseuille flow of the phonon gas as first discussed by Sussmann and Thellung. An equation for the thermal conductivity which correctly includes this phenomenon is found. Using this equation, the possible outcomes of steady-state thermal-conductivity measurements are discussed in terms of the microscopic scattering rates. Heat-pulse propagation is discussed from a similar point of view. The existence of Poiseuille Row in steady-state thermal-conductivity measurements bears directly on the possibility of observing second sound in solids. A quantitative analysis of available data on LiF suggests that the chemical purity of these samples sets very stringent limits on the observation of either of these effects. The observation of Poiseuille How in solid He' samples by Mezov-Deglin strongly suggests that this material is a prime subject for investigations of second-sound propagation.

We have studied thermodynamic and seme dynamic properties of a onedimensional model system whose displacement field Hamiltonian is strongly anharmonic, and is representative of those used to study displacive phase transitions. By studying the classical equations of motion, we find important solutions (domain walls) which cannot be represented effectively by the usual phonon perturbation expansions. The thermodynamic properties of this system can be calculated exactly by functional integral methods. No Hartree or decoupling approximations are made nor is a temperature dependence of the Hamiltonian introduced artificially. At low temperature, the thermodynamic behavior agrees with that found from a phenomenological model in which both phonons and domain walls-are included as elementary excitations. We then show that equal time correlation functions, calculated by both functional integral and phenomenological methods agree, and that the dynamic correlation functions (calculated only phenomenologically) exhibit a spectrum with both phonon peaks and a central peak due to domain wall motion.