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 ($W_1$) and next-nearest-neighbor ($W_2$) density–density intersite interactions. The variational approach treating the $U$ term exactly and the $W_l$ 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 $W_1>0$ and $W_2<0$. Two different types of charge-order (i.e., DCO and TCO phases) within $\sqrt{3}\times \sqrt{3}$ 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 $W_2<0$ 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 $\left|W_2\right|/W_1$ is investigated. It is found that some of the PS states are stable only at $T>0$. Two different critical values of $\left|W_2\right|/W_1$ 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.

原子极限下的扩展哈伯德模型，相当于点阵 $秒=1/2$费米子气体，被考虑在三角晶格上。该模型包括现场哈伯德$你$ 交互和最近邻（${宽}_1$) 和下一个最近的邻居 (${宽}_2$) 密度-密度点间相互作用。变分方法处理$你$ 准确的术语和 ${宽}_{升}$ 平均场近似中的项用于研究模型的热力学并找到其有限温度（$吨>0$) 相图（作为粒子浓度的函数） ${宽}_1>0$ 和 ${宽}_2<0$. 两种不同类型的充电顺序（即 DCO 和 TCO 阶段）$\sqrt{3}\times \sqrt{3}$单元格以及无序 (NO) 相出现在图中。此外，发现几种相分离 (PS) 状态（NO/DCO、DCO/DCO、DCO/TCO 和 TCO/TCO）对于固定浓度是稳定的。吸引人的${宽}_2<0$ 将 PS 状态稳定在 $吨=0$ 并将它们的发生区域扩展到 $吨>0$. 图表随着数量的增加而演变$\left|{宽}_2\right|/{宽}_1$被调查。发现一些 PS 状态仅在$吨>0$. 两个不同的临界值$\left|{宽}_2\right|/{宽}_1$ 为 PS 状态确定，其中两个相同类型的有序相（即 DCO 或 TCO 相的两个域）共存。