Evaluating the model (A 7.1) one finds that it describes a second order pha.se transition occurring for h = 0 and a critical value r = re. The transition is signaled by long range correlations of the spin field or power-type [Pg.118]

In the C °o limit, all the sites are bound the average correlation g(C is determined by the mth-order correlation function, which is 5 for the cyclic and 5 for the open linear system. This is true within the pairwise additive approximation for direct interaction, and neglecting long-range correlations. [Pg.241]

An important property of the Fermi surface is that the volume (in /c-space) that it encloses is not altered by the interaction between the electrons, unless long-range antiferromagnetic order is set up. This was first shown by Luttinger (1960). We shall make use of this theorem in Chapter 4, Section 3 in discussing metal-insulator transitions due to correlation. [Pg.72]

There has been much activity in the study of monolayer phases via the new optical, microscopic, and diffraction techniques described in the previous section. These experimental methods have elucidated the unit cell structure, bond orientational order and tilt in monolayer phases. Many of the condensed phases have been classified as mesophases having long-range correlational order and short-range translational order. A useful analogy between monolayer mesophases and die smectic mesophases in bulk liquid crystals aids in their characterization (see [182]). [Pg.131]

Therefore the model avoids two main difficulties the large amount of computer time which is normally needed for simulations and the loss of structural information which occurs in simple theoretical models (mean-field models) which do not take into account the structural aspects of the adsorbate layer. Mean-field-kind models fail in the prediction of phase transitions of the second order because at these points the long-range correlations appear. They also fail in describing the system s behaviour in the neighbourhood of the point of first-order kinetic phase transition. [Pg.564]

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