论文标题
三维$ o（n）\ otimes o（m）$模型中的相过渡：蒙特卡洛研究
Phase transition in the three-dimensional $O(N)\otimes O(M)$ model: a Monte Carlo study
论文作者
论文摘要
使用Monte Carlo模拟，我们考虑了$ O（n）\ otimes o（m）$ Sigma型号的晶格版本，价格为$ 2 \ leq m \ leq4 $和$ m \ leq n \ leq n \ leq8 $。我们发现$ n \ geq m+4 $的连续过渡。发现了二阶和弱一阶转换病例的关键指数的估计。对于$ m = 2 $，我们对指数的估计和边缘维度$ n_c^+（m）$与非扰动重新归一化组方法的结果非常吻合。对于$ m \ geq2 $，我们发现对大N扩展的第一和第二订单中获得的值之间的指数和边际维度的估计值。要完成图片，我们还考虑了通常的$ o（n）$型号（$ m = 1 $）。
Using Monte Carlo simulations, we consider the lattice version of the $O(N)\otimes O(M)$ sigma model for $2\leq M\leq4$ and $M\leq N \leq8$. We find a continuous transition for $N\geq M+4$. Estimates of the critical exponents for cases of second-order and weak first-order transitions are found. For $M=2$ our estimates of the exponents and marginal dimensionality $N_c^+(M)$ are in good agreement with the results of the non-perturbative renormalization group approach. For $M\geq2$ we find estimates of the exponents and marginal dimensionality between the values obtained in the first and second orders of the large-N expansion. To complete the picture, we also consider the usual $O(N)$ model ($M=1$).
