Chapter 11 Naive fermions critical critical fit NG \(\beta=5.75\) \(\rho=1.96\)

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 \(m_{cr}\)

\[\begin{gather} \chi^2/d.o.f.=1.81221 \\ P[0]=0.0300997\pm (0.0029) \\ P[1]=0.0630855\pm (0.0052) \\ P[2]=-0.513302\pm (0.032) \\ P[3]=-1.07862\pm (0.044) \\ P[4]=1.51362\pm (0.083) \\ P[5]=7.53226\pm (0.064) \\ P[6]=3.41669\pm (0.39) \\ P[7]=-13.0076\pm (0.96) \\ \end{gather}\] {\[\begin{gather} C=\begin{pmatrix} 1& 0.00244& -0.00189& -0.00202& 0.00159& -0.000616& 0.000539& 0.000974\\ 0.00244& 1& -0.00103& -0.00443& 0.00259& -0.00118& 0.000811& 0.00123\\ -0.00189& -0.00103& 1& 0.00733& -0.00292& 0.00786& -0.00694& -0.0169\\ -0.00202& -0.00443& 0.00733& 1& -0.0121& 0.0212& -0.0252& -0.0134\\ 0.00159& 0.00259& -0.00292& -0.0121& 1& 0.02& -0.0205& -0.0457\\ -0.000616& -0.00118& 0.00786& 0.0212& 0.02& 1& -0.0435& -0.0207\\ 0.000539& 0.000811& -0.00694& -0.0252& -0.0205& -0.0435& 1& 0.113\\ 0.000974& 0.00123& -0.0169& -0.0134& -0.0457& -0.0207& 0.113& 1\\ \end{pmatrix} \end{gather}\]}