Quasi-long-range Order

An alternative picture was first introduced by Aharony and Pytte in the context of random magnets. In this picture the order parameter correlation function exhibits algebraic decay with distance instead. This situation, intermediate between SRO and LRO, has come to be known as quasi-long-range order (QLRO). The most well-known example of QLRO, due to Berezinsky and to Kosterlitz and Thouless occurs in the low temperature phase of the two-dimensional XY model. A number of recent theoretical and computational studies have supported this point of view in random spin systems in a higher dimensionality . 

Thus, instead of the true Imig-range order we have a quasi-long-range order with the density correlation function (5.41b) qualitatively shown in Fig. 5.23b. 

For L—yoo, this integral diverges with its area logarithmically, that is very slowly. Such a film has quasi-long-range order. 

Feldman DE (2000) Quasi-Long-Range Order in Nematics Confined in Random Porous Media Phys Rev Lett 84 4886-4889... 

The resulting order is referred to as quasi-long-range order. It provides a marginal case between true long-range positional order and short-range order. These various types of order are illustrated in Fig. 8. 

Fig. 8 Representation of correlation function, G(r), and X-ray intensity, /( ), for long-range order, algebraically decaying quasi-long-range order, and short-range order...

So far, we have assumed that the crosslinks pin the smectic layers at a number of points but do not disturb the smectic density wave. However, a sufficient large density of crosslinks might lead to layer distortions that could destroy the quasi-long-range order of ID lamellar lattices [130, 131]. The crosslinks are randomly functionalized into the polymer backbone, and local density variations lead to quenched random disorder. This manifests itself as a mechanical random field that disturbs local layer positions and orientations. The effect of crosslinks on the smectic layer structure can be introduced via a corrugated potential that penalizes deviations of crosslinks from the local layer positions [4,132] ... 

---