One step of the <Glauber dynamics> chooses a vertex $v$ uniformly and resamples its spin from its conditional <Ising model> distribution given all other spins. If the proposed new spin is $x$ and $S_v(\sigma)=\sum_{w\sim v}\sigma(w)$, its update probability is
$$
\frac1n
\frac{e^{\beta xS_v(\sigma)}}
{e^{\beta S_v(\sigma)}+e^{-\beta S_v(\sigma)}}
=\frac{1+\tanh\{\beta xS_v(\sigma)\}}{2n}.
$$

Solution

Past exam of the mathematics course of the University of Cambridge / 2022 / iii / Paper 215 / 2 / a / Solution

 Solution

ID: past-exam-of-the-mathematics-course-of-the-university-of-cambridge/2022/iii/paper-215/2/a/solution