Eberhard K. Riedel

Scaling approach to anisotropic magnetic systems statics

Scaling laws are stated for anisotropic magnetic systems, where the anisotropy parameters are either scaled or held fixed. Combining the two ways of scaling, the critical behavior of thermodynamic quantities in anisotropic systems is determined. Particular attention is drawn to the temperature range where the anisotropy becomes important, and to the dependence there of the different quantities on the anisotropy parameters. In a transverse magnetic field the phase transition of an anisotropic magnet takes place along aλ-line. Assuming the singular part of the free enthalpy to depend on the distance from theλ-line, anomalous corrections to the transverse susceptibility and magnetization are calculated. For an experimental verification of many of the results, experiments including a variation of the anisotropy parameters or a finite transverse field are necessary.

Crossover Phenomena, Critical and Tricritical Phase Transitions

A theory for tricritical phenomena proposed by Wegner and the author is described on an elementary level. The emphasis of the discussion is on (i) the differences between critical and tricritical phase transitions, (ii) the crossover phenomena that occur near tricritical points, and (iii) the determination of tricritical exponents, scaling fields and scaling functions. The results have been obtained by renormalization‐group techniques and a scaling field approach to crossover phenomena. The elements of these techniques are briefly explained.

Theory of Tricritical Phase Transitions

A theory for tricritical phase transitions in two‐component Systems (such as He3‐He4 mixtures and antiferromagnets in a uniform magnetic field) is reviewed. The theory is based on a three‐dimensional model for a class of tricritical points, which is solved by using the renormalization‐group approach. This yields all tricritical exponents (including logarithmic correction factors) and the tricritical scaling fields. The relations of the theory to a tricritical scaling approach and to tricritical experiments are also discussed.