Compass model

Abstract In a solid with orbital degree of freedom, an orbital configuration does not minimize simultaneously bond energies in equivalent directions. This is a kind of frustration effect which exists intrinsically in orbital degenerate system. We review in this paper the intrinsic orbital frustration effects in Mott insulating systems. We introduce recent our theoretical studies in three orbital models, i.e. the cubic lattice orbital model, the two-dimensional orbital compass model and the honeycomb lattice orbital model. We show numerical results obtained by the Monte-Carlo simulations in finite size systems, and introduce some non-trivial orbital states due to the orbital frustration effect. 

In Sect. 2, the microscopic model which describes the inter-site orbital interactions are introduced. In Sect. 3, the numerical study in the orbital model in a cubic lattice is presented. The non-trivial orbital states in the two-dimensional orbital compass model and the honeycomb lattice orbital model are introduced in Sects. 4 and 5, respectively. The last section is devoted to the summary of this paper. 

Although the orbital model in (5) is derived in a simple cubic lattice, it is shown that, in general, the several orbital models are represented in similar forms of the Hamiltonian. This will be shown, in the following sections, for the orbital compass model in a two dimensional square lattice and the honeycomb lattice orbital model. 

As a different kind of orbital models with the intrinsic frustration effect, we introduce, in this section, the orbital compass model in the two-dimensional square lattice [16,17,20-22]. This model is given by... 

Fig. 6 Dispersion relation of the orbital interaction of the two-dimensional orbital compass model in (11) represented in the BriUouin zone for the square lattice...

We examine the orbital compass model by utilizing the quantum Monte-Carlo method is a finite-size cluster [4], The simulations have been performed on a square lattice of Lx L sites with periodic-boundary conditions. 

Teutschbein C, Seibert J (2010) Regional climate models for hydrological impact studies at the catchment scale a review of recent model strategies. Geogr Compass 4(7) 834—860... 

Using the NOAA ARL air-mass trajectory model, the WATOX researchers stratified volume-weighted averages of precipitation composition by compass sector. The results of these stratifications for excess S0 (Figure 6) showed that Bermuda was an ideal sampling platform for air that, at times, was directly impacted by anthropogenic tical uncertainties. standard error of... 

COMPASS has been used to model a number of condensed-phase organic systems.57-59 Hence, we chose COMPASS as a likely candidate for modeling fulvic and humic acids however, we caution the reader that classical mechanical force fields may be accurate for one system and not for another. The force field must be tested for each new application before the results can be considered reliable. 

The second approach was to employ periodic boundary conditions and molecular mechanics (COMPASS) to model the solvated SFA.55 73 These simulations were performed with Cerius2 4.2 (Accelrys, Inc.). Periodic boundary conditions create a bulk system with no surface effects and hence, this situation is more realistic compared to the experimental system of SFA dissolved in water. H20 molecules, however, must diffuse to allow motion of the SFA model, so that the SFA model conformations may be restricted due to this limited motion of the surrounding H20 molecules. Note also that periodic simulations must be charge neutral within the... 

FIGURE 5.8 Model of SFA with a -4 charge in a periodic box of 1493 H20 molecules and charge balanced with four Na+ ions after 50 ps of MD simulation with the COMPASS force field in Cerius2 (Accelrys, Inc.). Results of deprotonation and solvation are similar in these three-dimensional periodic simulations to the nonperiodic energy minimization in Figure 5.7(c). 

The X-ray structures of quartz and calcite were obtained from the FIZ Karlsruhe ICSD database [76]. The chosen model structures were constructed in MATERIALS STUDIO [77] under periodic boundary conditions and were then energy-minimized using the program DISCOVER with COMPASS force field until a maximum derivative better than 0.01 kcal mor A was achieved. 

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