For[r=0.001,r<2,r=r+0.025,
m=m+1;
Rang=N[-Log[r/2]+6];
the[n_]:=-Rang+2*Rang/M*n;
W[t_]:= r Cosh[t];
f[t_]:=-((4 (Sqrt[3]) Cosh[t])/(1+2 Cosh[2 t]));

e=Table[W[the[n]],{n,0,M}];
enew=Table[W[the[n]],{n,0,M}];

For[j=0,j<Iter,j++,
L=Interpolation[Table[{the[n],Log[1+Exp[-e[[n+1]]]]},{n,0,M}]];
For[n=0 ,n≤M,n++,enew[[n+1]]=N[W[the[n]]-(1/(2 Pi))NIntegrate[f[the[n]-t]L[t],{t,-Rang,Rang}]]];
For[n=0 ,n≤M,n++,e[[n+1]]=enew[[n+1]]];
]
L=Interpolation[Table[{the[n],Log[1+Exp[-e[[n+1]]]]},{n,0,M}]];
 c=3 r / Pi^2 NIntegrate[Cosh[t]L[t],{t,-Rang,Rang}];
TT[[m]][[2]]=c;
TT[[m]][[1]]=r;
]
TT
TT2:=Table[{Log[TT[[j]][[1]]/2],TT[[j]][[2]]},{j,1,Length[TT]}]
Plot[L[x],{x,-Rang,Rang},PlotStyle->{{Blue,Thick},{Red,Thick}},BaseStyle->{FontWeight->"Normal",FontSize->18},Frame->True,FrameLabel->{{"L(θ)",""},{"θ","R=2"}}]