Chapter 12 Naive fermions critical critical fit NG $\beta=5.85$ $\rho=1.96$

we fit $m_{PCAC}$ and $M_{PS}^2$ with the formule

$$\begin{cases} 2m_{PCAC}Z_V G_{PS}=P[0] + P[2] (\eta- \eta_{cr}) + P[4] \mu + P[7](\eta- \eta_{cr})\mu\\ M_{PS}^2=P[1] + P[3] (\eta- \eta_{cr}) + P[5] \mu+ P[6] (\eta- \eta_{cr})^2\,. \end{cases}$$

The coefficient $P[0]$ and $P[1]$ represent the value of $m_{PCAC}$ and $M_{PS}^2$ at $\eta_{cr}$ and $\mu=0$. We are assuming that we are simulating at $m_{cr}$

$$\begin{gather} \chi^2/d.o.f.=2.16209 \\ P[0]=0.0199683\pm (0.0019) \\ P[1]=0.0602006\pm (0.0075) \\ P[2]=-0.384093\pm (0.014) \\ P[3]=-1.75181\pm (0.16) \\ P[4]=0.653321\pm (0.042) \\ P[5]=6.88233\pm (0.043) \\ P[6]=16.7324\pm (1.2) \\ P[7]=-6.80453\pm (0.54) \\ \end{gather}$$ { $$\begin{gather} C=\begin{pmatrix} 1& 0.00181& -0.00104& -0.00175& 0.00138& -0.000242& 0.000362& -2.76e-06\\ 0.00181& 1& -0.00177& -0.00721& 0.00534& -0.000983& 0.00167& -0.000561\\ -0.00104& -0.00177& 1& 0.0042& -0.00233& 0.00426& -0.00445& -0.00412\\ -0.00175& -0.00721& 0.0042& 1& -0.0991& 0.0401& -0.0722& 0.00127\\ 0.00138& 0.00534& -0.00233& -0.0991& 1& -0.0011& -0.00263& -0.0287\\ -0.000242& -0.000983& 0.00426& 0.0401& -0.0011& 1& -0.0301& 0.00021\\ 0.000362& 0.00167& -0.00445& -0.0722& -0.00263& -0.0301& 1& 0.181\\ -2.76e-06& -0.000561& -0.00412& 0.00127& -0.0287& 0.00021& 0.181& 1\\ \end{pmatrix} \end{gather}$$ }