Critical Dynamics in Spin Glasses and Dilute Magnets

Available from UMI in association with The British Library. Requires signed TDF. We investigate dynamic critical phenomena in random magnetic systems. The transverse dynamics of a vector spin glass chain is studied by different scaling techniques. A nontrivial dynamic exponent is found which implies that the system at zero temperature has dynamic critical behaviour, in contradiction to previous work. Decimation is used and though approximate already implies critical behaviour. A new, exact, transfer matrix scaling technique is then applied yielding the dynamic critical exponent z = 3/2. Further insight into the spin glass dynamics is obtained also by a new numerical scaling technique which provides an analysis of the nature of the spin excitations. For very low frequencies we find that the states are all localised. Moreover it is shown that the localisation length is the characteristic length for the scaling of the spin excitation frequency. A relation between the dynamic critical exponent and static exponents for spin glasses is derived using crossover arguments. By evaluating the static critical properties this leads to the same nontrivial result for the dynamic exponent. A microscopic analysis of the implications of frustration for the scaling of vector spin glasses is given which show the need to generalise existing treatments. The new transfer matrix scaling technique is generalised to treat the dynamics of random spin systems in a field. Exact results for the dynamic and crossover exponents of one dimensional Heisenberg, transverse XY and Ising systems involving spin glass and random field disorder are then obtained. An exact calculation of the density of states of a dilute Heisenberg spin glass chain is also given using a superimposition method. The resulting form exhibits dynamic scaling. A regular fractal model is used to study the critical spin wave dynamics of dilute ferromagnetic and antiferromagnetic Heisenberg systems. Dynamic critical exponents and spectral dimensionalities are calculated. Exploiting the multiparameter dynamic scaling we present an explicit derivation of a relation between the dynamic critical exponent and static exponents for dilute ferromagnets. Generalisations of a recursive method to compute densities of states of self -similar systems involving multiparameter scaling are also proposed. Some implications of critical dynamics for static thermal properties are investigated. It is shown that the crossover from hydrodynamic to critical spin wave dynamics in dilute Heisenberg ferromagnets induces a crossover in properties such as magnetisation, specific heat and susceptibility. This crossover is in addition to the usual percolation-thermal crossover. Further crossover effects appear in the presence of a magnetic field. The low-temperature ordering of Heisenberg spins in fractal aggregates is also examined. Finite-size and dynamic crossover effects are discussed. It is shown that the critical temperature vanishes for infinitely large aggregates due to the reduced spectral dimensionality of the critical modes.