Chapter 10 Naive fermions critical fit W $\beta=5.95$ $\rho=1.96$

10.0.0.1 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 $$\eta_{cr}=P[0]$$

10.0.1 tau=2

$$\begin{gather} \chi^2/d.o.f.=0.0240056 \\ P[0]=-1.137\pm (0.0016) \\ P[1]=-0.984701\pm (0.004) \\ P[2]=-0.0232567\pm (0.058) \\ \end{gather}$$ { $$\begin{gather} C=\begin{pmatrix} 1& -1.92e-05& -0.000928\\ -1.92e-05& 1& -0.000145\\ -0.000928& -0.000145& 1\\ \end{pmatrix} \end{gather}$$ }

10.0.2 tau=3

$$\begin{gather} \chi^2/d.o.f.=0.0123019 \\ P[0]=-1.14567\pm (0.0021) \\ P[1]=-0.98772\pm (0.0053) \\ P[2]=-0.045688\pm (0.07) \\ \end{gather}$$ { $$\begin{gather} C=\begin{pmatrix} 1& -0.000273& -0.00104\\ -0.000273& 1& -8.05e-05\\ -0.00104& -8.05e-05& 1\\ \end{pmatrix} \end{gather}$$ }

10.0.3 tau=4

$$\begin{gather} \chi^2/d.o.f.=0.00932496 \\ P[0]=-1.14646\pm (0.0025) \\ P[1]=-0.987346\pm (0.007) \\ P[2]=-0.0288887\pm (0.079) \\ \end{gather}$$ { $$\begin{gather} C=\begin{pmatrix} 1& -0.000436& -0.0011\\ -0.000436& 1& 0.000474\\ -0.0011& 0.000474& 1\\ \end{pmatrix} \end{gather}$$ }

10.0.4 tau=5

$$\begin{gather} \chi^2/d.o.f.=0.00919778 \\ P[0]=-1.14632\pm (0.003) \\ P[1]=-0.987246\pm (0.0091) \\ P[2]=-0.00213908\pm (0.095) \\ \end{gather}$$ { $$\begin{gather} C=\begin{pmatrix} 1& -0.000201& -0.00134\\ -0.000201& 1& 0.00116\\ -0.00134& 0.00116& 1\\ \end{pmatrix} \end{gather}$$ }

10.0.5 tau=6

$$\begin{gather} \chi^2/d.o.f.=0.0101053 \\ P[0]=-1.14591\pm (0.0037) \\ P[1]=-0.989967\pm (0.011) \\ P[2]=0.0166431\pm (0.12) \\ \end{gather}$$ { $$\begin{gather} C=\begin{pmatrix} 1& 0.000128& -0.00176\\ 0.000128& 1& 0.00156\\ -0.00176& 0.00156& 1\\ \end{pmatrix} \end{gather}$$ }

10.0.6 Table

##   tau   eta_cr    deta_cr
## 1   2 -1.13700 0.00160136
## 2   3 -1.14567 0.00205826
## 3   4 -1.14646 0.00249327
## 4   5 -1.14632 0.00297879
## 5   6 -1.14591 0.00372412