we perform a MC optimization to obtain optimal values for the two new parameters. This procedure is repeated until the desired convergence is achieved. In each step the lattice size is increased by one point while we include two new parameters.

We use the Metropolis algorithm to find the optimal values for $x_p(i)$ and $\alpha(i+1)$ in each step. For every trial in the $i$-th turn we assume that $x_p(i)$ and $\alpha(i+1)$ follow a uniform distribution in $(0,1)$ and $(0,\infty)$, respectively (in practice the interval $(0,\infty)$ is replaced by the finite one $(0,c)$ with an upper cutoff $c>>1$). The annealing is introduced through a thermalized probability distribution of the type: $P=e^{-K[h_f]/T}$ to avoid the trapping into local minima. The parameter $T$, playing the role of the temperature, is positive and has to be tuned adiabatically to smaller and smaller values such that the global minimum is reached asymptotically.

We do not keep the values of the old fit-parameters fixed in the following step. Instead we relax this constraint using Gaussian distributed random variables for the choice of the old fit-parameters. The mean values of these Gaussians are the optimum values obtained for these parameters in the previous step and the corresponding 