Criticality of Pure and Random Systems

The theory of critical phenomena has reached nowadays a high level. The concepts of the scale invariance and universality are understood in principle as consequences of the interaction of critical fluctuations at the critical point. A theoretical description of critical systems further away from the phase transition point can be performed and good agreement with available experiments is reached. However, studying more complex systems one meets certain discrepancies between theoretical predictions and experimental observations. An example is given by the static critical behavior in presence of structural disorder as observed for fluids in porous medium in the vicinity of the critical point or by the presence of a complicated symmetry of the order parameter as for the Potts model. Also some experimental results in the critical dynamics remain to be understood. Neutron and light scattering are the experimental methods to analyze dynamical correlations of the critical fluctuations. In such a fundamental system as the Heisenberg antiferromagnet the experiment shows that the maximal scattering intensity occurs at zero energy transfer at the phase transition point, theory however predicts this peak at a finite energy transfer. In this project this discrepancy will be resolved. The theoretical approach makes it also possible to compute the light scattering intensity and to compare it with experiments at the superfluid phase transition. Further problems in the field of static and dynamic critical phenomena will be treated. An analytical study performed by means of the field-theoretical methods will be accomplished by numerical simulations of the systems of interest. This will allow on the one hand examining the analytic results of the models and on the other hand testing their applicability for the physical systems.

The theory of critical phenomena has reached nowadays a high level. The concepts of the scale invariance and universality are understood in principle as consequences of the interaction of critical fluctuations at the critical point. A theoretical description of critical systems further away from the phase transition point can be performed and good agreement with available experiments is reached. However, studying more complex systems one meets certain discrepancies between theoretical predictions and experimental observations. An example is given by the static critical behavior in presence of structural disorder as observed for fluids in porous medium in the vicinity of the critical point or by the presence of a complicated symmetry of the order parameter as for the Potts model. Also some experimental results in the critical dynamics remain to be understood. Neutron and light scattering are the experimental methods to analyze dynamical correlations of the critical fluctuations. In such a fundamental system as the Heisenberg antiferromagnet the experiment shows that the maximal scattering intensity occurs at zero energy transfer at the phase transition point, theory however predicts this peak at a finite energy transfer. In this project this discrepancy will be resolved. The theoretical approach makes it also possible to compute the light scattering intensity and to compare it with experiments at the superfluid phase transition. Further problems in the field of static and dynamic critical phenomena will be treated. An analytical study performed by means of the field-theoretical methods will be accomplished by numerical simulations of the systems of interest. This will allow on the one hand examining the analytic results of the models and on the other hand testing their applicability for the physical systems.