欧拉键立方模型的普遍临界性质
Universal critical properties of the Eulerian bond-cubic model
摘要：
本文采用有效的聚类算法和有限尺寸标度分析，通过蒙特卡罗模拟研究了正方形晶格上的欧拉键立方模型。对于不同的$n$值，确定了模型的临界点和四个临界指数。其中两个指数是分形维数，这是第一次得到的数值。我们的结果与库仑气体对$n < 2$的临界O（$n$）分支的预测和以前的转移矩阵计算结果一致。对于$n=2$，我们发现最大临界欧拉键组元的热指数、磁指数和分维与临界O（2）圈模型的结果不同。这些结果证实，立方各向异性在$n=2$处是边缘的，但与$n<2$无关。
英文摘要：
We investigate the Eulerian bond-cubic model on the square lattice by means of Monte Carlo simulations, using an efficient cluster algorithm and a finite-size scaling analysis. The critical points and four critical exponents of the model are determined for several values of $n$. Two of the exponents are fractal dimensions, which are obtained numerically for the first time. Our results are consistent with the Coulomb gas predictions for the critical O($n$) branch for $n < 2$ and the results obtained by previous transfer matrix calculations. For $n=2$, we find that the thermal exponent, the magnetic exponent and the fractal dimension of the largest critical Eulerian bond component are different from those of the critical O(2) loop model. These results confirm that the cubic anisotropy is marginal at $n=2$ but irrelevant for $n<2$.
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