Academic literature on the topic 'Diluted spin systems'

This chapter illustrates basic concepts of quantum integrable systems on two important models of statistical physics: the Q-state Potts model and the O(n) model. Both models are transformed into loop and vertex models that provide representations of the dense and dilute Temperley–Lieb algebras. The identification of the corresponding integrable R-matrices leads to the solution of both models by the algebraic Bethe Ansatz technique. Elementary excitations are discussed in the critical case and the link to conformal field theory in the thermodynamic limit is established. The concluding sections outline the solution of a specific model of the theta point of collapsing polymers, leading to a continuum limit with a non-compact target space.

In this chapter, we discuss adsorption phenomena in supercritical systems, a situation that occurs in many application areas in chemical-process and materials engineering. An example of a commercial application in this area, which has achieved wide acceptance as a tool in analytical chemistry, is supercritical fluid chromatography (SFC). Not only is SFC a powerful technique for chemical analysis, but it also is a useful method for measuring transportive and thermodynamic properties in the near-critical systems. In the next section, we analyze adsorption-column dynamics using simple dynamic models, and describe how data from a chromatographic column can be used to estimate various thermodynamic and transport properties.We then proceed to discuss the effects of proximity to the critical point on adsorption behavior in these systems. The closer the system is to its critical point, the more interesting is its behavior. For very dilute solute systems, like those considered here, the energy balance is often ignored to a first approximation; this leads to a simple set of mass-balance equations defining transport for each species. These equations can be developed to various levels of complexity, depending upon the treatment of the adsorbent (stationary phase). The conceptual view of these phases can span a wide range of possibilities ranging from completely nonporous solids (fused structures) to porous materials with complicated ill-defined pore structures. Given these considerations, it is customary to make the following assumptions in the development of a simple model of adsorber-bed dynamics: . . .1. The stationary and mobile phases are continuous in the direction of the flow, with the fluid phase possessing a flat velocity profile (“plug” flow).. . . . . . 2. The porosity of the stationary phase is considered constant irrespective of pressure and temperature conditions (i.e., it is incompressible). . . . . . .3. The column is considered to be radially homogeneous, leading to a set of equations with one spatially independent variable, representing distance along the column axis. . . . . . . 4. The dispersion term in the model equation represents the combined effects of molecular diffusion and dispersion due to convective stirring in the bed. These effects are combined into an effective phenomenological dispersion coefficient, considered to be constant throughout the column. . . .

Following a brief review of laser frequency and time domain techniques for overcoming inhomogeneous broadening of optical transitions in solids, recent studies on the failure of the optical Bloch equations (OBE) in describing saturation and coherent transient phenomena in ruby will be discussed. Experiments using free induction decay (FID), as in the original work on the system Pr3+:LaF3 by DeVoe and Brewer1, as well as extensions to rotary echos2 and hole-burning3 will be described. At low fields (~ 0.4 T), the time and frequency domain linewidth variation with Rabi frequency agree provided c