SciCode / 47.4 / Write a function to use Markov Chain Monte Carlo simulation to generate samples…

Background:

In the canonical ensemble, we have to sample distribution. This can be done using the following scheme:
Select a particle at random and calculate the energy of this configuration U(0).
2. Give this particle a random displacement,
r(o)→r(0)+Δ(Ranf−0.5),
where Δ/2 is the maximum displacement. The value of Δ should be chosen such that the sampling scheme is optimal. The new configuration is denoted n and its energy U(n).

3. The move is accepted with a probability
acc(o→n)=min(1,exp{−β[U(n)−U(o)]})
If rejected, the old configuration is kept.

Background:

In the canonical ensemble, we have to sample distribution. This can be done using the following scheme:
Select a particle at random and calculate the energy of this configuration $\mathcal{U}(0)$.
2. Give this particle a random displacement,
$$
\mathbf{r}(\mathbf{o}) \rightarrow \mathbf{r}(\mathbf{0})+\Delta(\operatorname{Ranf}-0.5),
$$
where $\Delta / 2$ is the maximum displacement. The value of $\Delta$ should be chosen such that the sampling scheme is optimal. The new configuration is denoted $n$ and its energy $\mathcal{U}(n)$.

3. The move is accepted with a probability
$$
\operatorname{acc}(o \rightarrow \mathfrak{n})=\min (1, \exp \{-\beta[\mathcal{U}(\mathfrak{n})-\mathcal{U}(o)]\})
$$
If rejected, the old configuration is kept.