Magnetic properties, near criticality

The application of the RG is the subject of a recent introductory review, which whilst couched in terms of criticality near to magnetic phase transitions, explains scaling, and also the importance of universality viz. that certain critical exponents, i.e. properties near a phase transition depend only upon for example the number of spatial dimensions and the range of interactions, and not upon the nature of the physical phenomenon itself (see also ref. 24). 

The magnetic properties of US depend strongly on pressure (Huang et al. 1979) or on fission damage (Matsui et al. 1983). Sample dependence was found by Aldred and Trod (1983) in magnetic studies of the critical behaviour near the Curie temperature. 

Supercritical fluids (SCFs) offer the potential for a controlled solution environment because of the tunability of their properties by small changes in temperature and pressure. Indeed, near-critical water and supercritical water are obvious candidates as solvents in nanoparticle formation because water is the most commonly used solvent in conventional synthesis of inorganic particles. However, other solvents, such as carbon dioxide, can also be used. Several methods that take advantage of SCF behavior are described below. Not all have been employed in the production of magnetic nanoparticles. However, they represent a natural bridge between methods that are carried out mainly in the liquid state and those that are carried out in the gaseous state. 

Not only do the thermodynamic properties follow similar power laws near the critical temperatures, but the exponents measured for a given property, such as heat capacity or the order parameter, are found to be the same within experimental error in a wide variety of substances. This can be seen in Table 13.3. It has been shown that the same set of exponents (a, (3, 7, v, etc.) are obtained for phase transitions that have the same spatial (d) and order parameter (n) dimensionalities. For example, (order + disorder) transitions, magnetic transitions with a single axis about which the magnetization orients, and the (liquid + gas) critical point have d= 3 and n — 1, and all have the same values for the critical exponents. Superconductors and the superfluid transition in 4He have d= 3 and n = 2, and they show different values for the set of exponents. Phase transitions are said to belong to different universality classes when their critical exponents belong to different sets. 

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