硬方格子气体的Husimi格点解及其相干反常方法分析
Husimi lattice solutions and the coherent-anomaly-method analysis for hard-square lattice gases
摘要：
虽然由$k$ NN粒子组成的晶格气体，禁止其$k$次近邻被占据，已在文献中得到广泛的研究，在正方形晶格上的2NN模型中的流体-柱状转变的位置和普适类仍然是一个有争议的话题。在这里，我们提出了这个模型的巨正则解的Husimi格与对角正方形格，$2L(L+1)$网站，$L \leqslant 7$。平均场解的系统序列证实了该系统中存在一个连续的过渡，并将临界化学势$μ_{2,c}(L)$和粒子密度$ρ_{2,c}(L)$外推到$L \rightarrow \infty$，得到了这些量的估计值，与以前的正方形晶格上的2NN模型的结果非常一致。为了确认这种方法的可靠性，我们采用它也为1 NN模型，其中非常准确的估计的关键参数$μ_{1,c}$和$ρ_{1,c}$ -在这个模型中的流体-固体过渡的正方形晶格-被发现从外推的数据$L \leqslant 6$。通过相干反常方法（CAM）研究了这些跃迁的非经典临界指数，在1 NN情况下，得到的$β$和$ν$与预期的伊辛指数相差不超过6%.对于2NN模型，CAM分析有些不确定，因为指数明显依赖于用于计算它们的$μ_{2,c}$的值。尽管如此，我们的研究结果表明，$β$和$ν$是相当大的Ashkin-Teller指数在2NN系统的数值研究报告。
英文摘要：
Although lattice gases composed by $k$NN particles, forbidding up to their $k$th nearest neighbors of being occupied, have been widely investigated in literature, the location and the universality class of the fluid-columnar transition in the 2NN model on the square lattice is still a topic of debate. Here, we present grand-canonical solutions of this model on Husimi lattices built with diagonal square lattices, with $2L(L+1)$ sites, for $L \leqslant 7$. The systematic sequence of mean-field solutions confirms the existence of a continuous transition in this system and extrapolations of the critical chemical potential $μ_{2,c}(L)$ and particle density $ρ_{2,c}(L)$ to $L \rightarrow \infty$ yield estimates of these quantities in close agreement with previous results for the 2NN model on the square lattice. To confirm the reliability of this approach we employ it also for the 1NN model, where very accurate estimates for the critical parameters $μ_{1,c}$ and $ρ_{1,c}$ -- for the fluid-solid transition in this model on the square lattice -- are found from extrapolations of data for $L \leqslant 6$. The non-classical critical exponents for these transitions are investigated through the coherent anomaly method (CAM), which in the 1NN case yields $β$ and $ν$ differing by at most 6\% from the expected Ising exponents. For the 2NN model, the CAM analysis is somewhat inconclusive, because the exponents sensibly depend on the value of $μ_{2,c}$ used to calculate them. Notwithstanding, our results suggest that $β$ and $ν$ are considerably larger than the Ashkin-Teller exponents reported in numerical studies of the 2NN system.
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