Chapter 13 Naive fermions critical critical fit NG \(\beta=5.95\) \(\rho=1.96\)

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 \(m_{cr}\)

\[\begin{gather} \chi^2/d.o.f.=0.241693 \\ P[0]=0.00983435\pm (0.00097) \\ P[1]=0.0263367\pm (0.0025) \\ P[2]=-0.32842\pm (0.015) \\ P[3]=-0.870766\pm (0.04) \\ P[4]=0.240895\pm (0.013) \\ P[5]=5.71531\pm (0.042) \\ P[6]=6.90876\pm (0.14) \\ P[7]=1.90815\pm (0.31) \\ \end{gather}\] {\[\begin{gather} C=\begin{pmatrix} 1& 0.000817& -0.000445& -0.000825& 1.82e-05& -0.000219& -5.39e-05& -8.19e-05\\ 0.000817& 1& 3.83e-05& -0.00242& -0.000655& -0.000419& 0.000149& 0.000254\\ -0.000445& 3.83e-05& 1& 0.000196& -0.0106& 0.0043& 0.00311& 0.00345\\ -0.000825& -0.00242& 0.000196& 1& 0.0102& 0.00616& -0.00568& -0.00394\\ 1.82e-05& -0.000655& -0.0106& 0.0102& 1& 0.00132& -0.0017& 0.00103\\ -0.000219& -0.000419& 0.0043& 0.00616& 0.00132& 1& 0.00973& 0.0166\\ -5.39e-05& 0.000149& 0.00311& -0.00568& -0.0017& 0.00973& 1& 0.0345\\ -8.19e-05& 0.000254& 0.00345& -0.00394& 0.00103& 0.0166& 0.0345& 1\\ \end{pmatrix} \end{gather}\]}