Ising magnets

The coverage d then is simply related to the magnetization m of the Ising magnet,... 

Unfortunately, the presence of the term in Eq. (5) makes it much more difficult to extract the equilibrium S J) behavior than it was to find (p T) for an Ising magnet. However, the general approach is the same— fmd the S value at which dQdS= 0 and G is a global minimum. The temperature dependence of 5arising from Eq. (5) for a nematic liquid crystal turns out to be quite complicated since there is no analytic solution to the quartic equation arising from 5 QdS = 0. However, the behavior of 5( 7) for 7 < 7j can still be very well approximated by a power-law expression ... 

From Eq. (4.53) we obtain the corresponding partition function of the Ising magnet by replacing H by its counterpart H given in Eq. (4.57), where,... 

The previous section reviewed the elements of statistical mechanics that are important in thinking about the structures, fluctuations, and phase behavior of surfaces, interfaces, and membranes. In this section, we consider an important application of these ideas to the problem of phase separation in binary mixtures. This problem is analogous to other types of phase transitions, such as those found in Ising magnets. It is important to understand the specific problem of phase separation because it is this phenomenon that results in the equilibrium between two coexisting states, which naturally gives rise to the existence of interfaces. 

In this chapter, we have discussed a simple kinetic formulation of Ising magnets based on nonequilibrium thermodynamics. We start with the simplest relaxation equation of the irreversible thermodynamics with a characteristic time and mention a general formulation based on the research results in the literature for some well known dynamic problems with more than one relaxational processes. Recent theoretical findings provide a more precise... 

Fig. 42. Phase diagram for LiHo,Y, F4 Ising magnet. PM, paramagne FM, ferromagnet SG, spin glass. Experimental data are from neutron scattering and magnetic susceptibility measurements (Kjaer et al. 1989, Reich et al. 1990).

In condensed matter physics, the effects of disorder, defects, and impurities are relevant for many materials properties hence their understanding is of utmost importance. The effects of randomness and disorder can be dramatic and have been investigated for a variety of systems covering a wide field of complex phenomena [109]. Examples include the pinning of an Abrikosov flux vortex lattice by impurities in superconductors [110], disorder in Ising magnets [111], superfluid transitions of He in a porous medium [112], and phase transitions in randomly confined smectic liquid crystals [113, 114]. 

A. 0. Parry and R. Evans, Novel phase behaviour of a confined fluid or Ising magnet, PhysicaA, 181, 2 50-2 96 (199 23. 

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