Order, long-range parameter

A switch to double-angle vectors given by Eq. (2.3.12) not only significantly simplifies the treatment of orientation phase transitions in planar systems of nonpolar molecules but also leads to a number of substantial inferences on the transition nature. First of all note that the long-range-order parameter t] (vanishing in a disordered phase and equal to unity at T = 0) in a -dimensional space (specified by the orientations of long molecular axes) can be defined as ... 

The equilibrium value of the long-range order parameter, is obtained by the conditions... 

Show that the long-range order parameter for domain 1 is the negative of the long-range order parameter of domain 2. 

How could we take into account the fluctuations of the order parameter Let us return to the well-studied example of the gas-liquid system. A general equation of the state of gases and liquids proved in statistical physics [9] has a form p = nk T - n2G(x) where G(x) is some integral containing the interaction potential of particles and the joint correlation function x(r). Therefore, the equation for the long-range order parameter n contains in itself the functional of the intermediate-order parameter x r)-... 

There is a long-range order parameter, s, defined as the fraction of A atoms, J a, occupying the correct sites minus the fraction occupying the wrong sites ... 

Long-range order parameter, s, decreases with temperature. 

Figure 14. Irradiation and disorder (left) long-range order parameter S as a function of the fluency for a disorder FePt (50 nm)-Pt (001) thin film (starting SKI) and particularly ordered one (starting S=0.4) and (right) Polar Kerr measurements of three irradiated CrPt3 areas with N+ ions with a fluency in the range 2xl015 -2xl016 ions/cm2.

At low temperatures, the long-range order in AuCus is virtually perfect but, as Tc is approached, some randomness sets in. This departure from perfect order can be described by means of the long-range order parameter S, defined as follows ... 

Fig. 13-4 Variation of the long-range order parameter S with temperature, for AuCus and CuZn. (AuCua from Keating and Warren [13.2] CuZn data from Chipman and Warren [13.3]).

Magnetic properties of Pt, xCrx alloys. o77 is the magnetization at 77 K, and S the long-range order parameter (Goto 1977). 

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