The product $\sigma_0\sigma_1\cdots\sigma_{2022}$ contains $2023$ spins and changes sign under the global spin flip $\sigma\mapsto-\sigma$. By part ii, the infinite-volume plus state is spin-flip symmetric. Therefore
$$
\langle\sigma_0\sigma_1\cdots\sigma_{2022}\rangle_{\beta,0}^{\mathbb Z,+}=0.
$$


Solution

Past exam of the mathematics course of the University of Cambridge / 2023 / iii / Paper 209 / 3 / iii / Solution

 Solution

ID: past-exam-of-the-mathematics-course-of-the-university-of-cambridge/2023/iii/paper-209/3/iii/solution