论文标题
三个维度的立方固定点：$ ϕ^4 $型号的蒙特卡洛模拟
Cubic fixed point in three dimensions: Monte Carlo simulations of the $ϕ^4$ model on the lattice
论文作者
论文摘要
我们通过使用适用于从简单的立方晶格上的$ n $ - 组件$ ϕ^4 $型号的数据来研究，以$ n = 3 $和$ 4 $的立方固定点的使用。我们将改进模型的思想推广到两参数模型家族。扫描了两个参数的空间，其中两个领先的缩放缩放消失的幅度的幅度幅度消失了。为此，引入了无量纲数量，该数量可以监视$ O（n）$ - 不变性的破坏。对于$ n = 4 $，我们确定校正指数$ω_1= 0.763（24）$和$ω_2= 0.082（5）$。在$ n = 3 $的情况下，我们获得$ y_4 = 0.0142（6）$，用于在$ O（3）$ - 不变的固定点处的Cutic扰动的RG-Exponent，而校正指数$ω_2= 0.0133（8）$在立方固定点处。接近改进点的模拟导致估计值$ν= 0.7202（7）$和$η= 0.0371（2）$ n = 4 $的立方固定点的关键指数的$。对于$ n = 3 $，在立方固定点上，$ o（3）$ - 对称性仅被损坏，关键指数仅与$ o（3）$ - 不变固定点的指数不同。我们发现$ -0.00001 \Lessapproxη_{Cubic} - η_{O（3）} \ Lessapprox 0.00007 $和$ν_{CUCIC} -K {O（3）} = -0.00061（10）$。
We study the cubic fixed point for $N=3$ and $4$ by using finite size scaling applied to data obtained from Monte Carlo simulations of the $N$-component $ϕ^4$ model on the simple cubic lattice. We generalize the idea of improved models to a two-parameter family of models. The two-parameter space is scanned for the point, where the amplitudes of the two leading corrections to scaling vanish. To this end, a dimensionless quantity is introduced that monitors the breaking of the $O(N)$-invariance. For $N=4$, we determine the correction exponents $ω_1=0.763(24)$ and $ω_2=0.082(5)$. In the case of $N=3$, we obtain $Y_4=0.0142(6)$ for the RG-exponent of the cubic perturbation at the $O(3)$-invariant fixed point, while the correction exponent $ω_2=0.0133(8)$ at the cubic fixed point. Simulations close to the improved point result in the estimates $ν=0.7202(7)$ and $η=0.0371(2)$ of the critical exponents of the cubic fixed point for $N=4$. For $N=3$, at the cubic fixed point, the $O(3)$-symmetry is only mildly broken and the critical exponents differ only by little from those of the $O(3)$-invariant fixed point. We find $-0.00001 \lessapprox η_{cubic}- η_{O(3)} \lessapprox 0.00007$ and $ν_{cubic}-ν_{O(3)} =-0.00061(10)$.
