Abstract
The extended Hubbard model in the atomic limit, which is equivalent to lattice S=1/2 fermionic gas, is considered on the triangular lattice. The model includes onsite Hubbard U interaction and both nearest-neighbor (W1) and next-nearest-neighbor (W2) density–density intersite interactions. The variational approach treating the U term exactly and the Wl terms in the mean-field approximation is used to investigate thermodynamics of the model and to find its finite temperature (T>0) phase diagrams (as a function of particle concentration) for W1>0 and W2<0. Two different types of charge-order (i.e., DCO and TCO phases) within 3×3 unit cells as well as the nonordered (NO) phase occur on the diagram. Moreover, several kinds of phase-separated (PS) states (NO/DCO, DCO/DCO, DCO/TCO, and TCO/TCO) are found to be stable for fixed concentration. Attractive W2<0 stabilizes PS states at T=0 and it extends the regions of their occurrence at T>0. The evolution of the diagrams with increasing of |W2|/W1 is investigated. It is found that some of the PS states are stable only at T>0. Two different critical values of |W2|/W1 are determined for the PS states, in which two ordered phases of the same type (i.e., two domains of the DCO or TCO phase) coexist.
Highlights
The classical lattice gas model is useful effective model for description of adsorbed particles on crystalline substrates
In the case of a graphine surface or a single layer of graphene as well as (111) face-centered cubic surface, the periodic potential of the underlying crystal surface forms a triangular lattice, which can be occupied by adsorbed atoms, e.g., [8,9,10,11,12]
Particular attention is taken for effects of the next-nearest-neighbor attraction on the phase diagrams at finite temperatures
Summary
At Tc∗1 the discontinuous change of concentration in the DCO phase domain of the PS1 state occurs This behavior is associated with a new first-order DCO-DCO boundary inside the DCO region [ending at a bicritical-end ( called as isolated-critical) point, cf [22, 24, 25, 37]], which is present on the diagram for fixed μ.
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