The <renormalization-group fixed points> are the zeros of the <beta function (physics)>:
$$
\boxed{g_0^*=0,
\qquad
g_c^*=\frac{2\pi\epsilon}{(N-2)\Lambda^\epsilon}}.
$$
For $N>2$ and $\epsilon>0$, the positive fixed point $g_c^*$ separates the low-temperature ordered flow toward $g=0$ from the high-temperature strong-coupling flow. At $\epsilon=0$ the two perturbative fixed points merge at zero.

Solution

Past exam of the mathematics course of the University of Cambridge / 2021 / iii / Paper 303 / 3 / e / Solution

 Solution

ID: past-exam-of-the-mathematics-course-of-the-university-of-cambridge/2021/iii/paper-303/3/e/solution