Chapter 8 Naive fermions critical fit W $\beta=5.75$ $\rho=1.96$

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

8.0.1 tau=2

$$\begin{gather} \chi^2/d.o.f.=0.0101487 \\ P[0]=-1.26153\pm (0.0028) \\ P[1]=-0.977204\pm (0.0072) \\ P[2]=0.205121\pm (0.086) \\ \end{gather}$$ { $$\begin{gather} C=\begin{pmatrix} 1& -0.000872& -8.85e-05\\ -0.000872& 1& -0.000383\\ -8.85e-05& -0.000383& 1\\ \end{pmatrix} \end{gather}$$ }

8.0.2 tau=3

$$\begin{gather} \chi^2/d.o.f.=0.0010876 \\ P[0]=-1.27828\pm (0.0044) \\ P[1]=-0.975728\pm (0.0098) \\ P[2]=0.314211\pm (0.11) \\ \end{gather}$$ { $$\begin{gather} C=\begin{pmatrix} 1& -0.00161& -0.000173\\ -0.00161& 1& -0.00129\\ -0.000173& -0.00129& 1\\ \end{pmatrix} \end{gather}$$ }

8.0.3 tau=4

$$\begin{gather} \chi^2/d.o.f.=0.00531205 \\ P[0]=-1.26973\pm (0.006) \\ P[1]=-0.983751\pm (0.011) \\ P[2]=0.376337\pm (0.14) \\ \end{gather}$$ { $$\begin{gather} C=\begin{pmatrix} 1& -0.000735& -0.00119\\ -0.000735& 1& 0.00051\\ -0.00119& 0.00051& 1\\ \end{pmatrix} \end{gather}$$ }

8.0.4 tau=5

$$\begin{gather} \chi^2/d.o.f.=0.00525624 \\ P[0]=-1.25499\pm (0.0085) \\ P[1]=-0.990844\pm (0.014) \\ P[2]=0.240153\pm (0.19) \\ \end{gather}$$ { $$\begin{gather} C=\begin{pmatrix} 1& -0.000485& -0.00162\\ -0.000485& 1& 0.00319\\ -0.00162& 0.00319& 1\\ \end{pmatrix} \end{gather}$$ }

8.0.5 tau=6

$$\begin{gather} \chi^2/d.o.f.=0.0183583 \\ P[0]=-1.24268\pm (0.0096) \\ P[1]=-0.993628\pm (0.017) \\ P[2]=0.0514147\pm (0.28) \\ \end{gather}$$ { $$\begin{gather} C=\begin{pmatrix} 1& 0.000622& -0.00159\\ 0.000622& 1& 0.0015\\ -0.00159& 0.0015& 1\\ \end{pmatrix} \end{gather}$$ }

8.0.6 Table

##   tau   eta_cr    deta_cr
## 1   2 -1.26153 0.00276674
## 2   3 -1.27828 0.00441189
## 3   4 -1.26973 0.00601452
## 4   5 -1.25499 0.00846617
## 5   6 -1.24268 0.00955908