Chapter 9 Naive fermions critical fit W $\beta=5.85$ $\rho=1.96$

9.0.0.1 Simplified fit local rawi

The fit formula with tau

$$\begin{cases} r_{AWI}=P[1] (\eta- \eta_{cr}) +P[2] \mu\\ \end{cases}$$ In the above fit we are treating $\eta_{cr}$ and $m_{cr}$ as fits parameters, so $$\eta_{cr}=P[0]$$

$$\begin{gather} \chi^2/d.o.f.=0.246525 \\ P[0]=-1.21126\pm (0.0074) \\ P[1]=-0.962676\pm (0.019) \\ P[2]=0.285741\pm (0.25) \\ \end{gather}$$ { $$\begin{gather} C=\begin{pmatrix} 1& -0.0037& -0.00312\\ -0.0037& 1& 0.0042\\ -0.00312& 0.0042& 1\\ \end{pmatrix} \end{gather}$$ }

9.0.1 tau=2

$$\begin{gather} \chi^2/d.o.f.=0.0387706 \\ P[0]=-1.19887\pm (0.0018) \\ P[1]=-0.985018\pm (0.0056) \\ P[2]=0.0501364\pm (0.065) \\ \end{gather}$$ { $$\begin{gather} C=\begin{pmatrix} 1& -0.000202& -0.000397\\ -0.000202& 1& -0.000291\\ -0.000397& -0.000291& 1\\ \end{pmatrix} \end{gather}$$ }

9.0.2 tau=3

$$\begin{gather} \chi^2/d.o.f.=0.0303209 \\ P[0]=-1.21478\pm (0.0033) \\ P[1]=-0.983972\pm (0.0087) \\ P[2]=0.0752283\pm (0.092) \\ \end{gather}$$ { $$\begin{gather} C=\begin{pmatrix} 1& -0.000477& 0.000143\\ -0.000477& 1& -0.00085\\ 0.000143& -0.00085& 1\\ \end{pmatrix} \end{gather}$$ }

9.0.3 tau=4

$$\begin{gather} \chi^2/d.o.f.=0.020064 \\ P[0]=-1.21437\pm (0.0046) \\ P[1]=-0.987487\pm (0.01) \\ P[2]=0.0993683\pm (0.13) \\ \end{gather}$$ { $$\begin{gather} C=\begin{pmatrix} 1& -0.00103& 0.000198\\ -0.00103& 1& -0.00205\\ 0.000198& -0.00205& 1\\ \end{pmatrix} \end{gather}$$ }

9.0.4 tau=5

$$\begin{gather} \chi^2/d.o.f.=0.246525 \\ P[0]=-1.21126\pm (0.0074) \\ P[1]=-0.962676\pm (0.019) \\ P[2]=0.285741\pm (0.25) \\ \end{gather}$$ { $$\begin{gather} C=\begin{pmatrix} 1& -0.0037& -0.00312\\ -0.0037& 1& 0.0042\\ -0.00312& 0.0042& 1\\ \end{pmatrix} \end{gather}$$ }

9.0.5 Table

##   tau   eta_cr    deta_cr
## 1   2 -1.19887 0.00177853
## 2   3 -1.21478 0.00329186
## 3   4 -1.21437 0.00456207
## 4   5 -1.20968 0.00565167