The O(n) ${\varphi }^4$ model with free surfaces in the large-$n$ limit: Some exact results for boundary critical behaviour, fluctuation-induced forces and distant-wall corrections

H. W. Diehl, S. B. Rutkevich

The $O(n)$ ${\varphi }^4$ model on a slab ${\mathbb{R}}^{d-1}\times [0,L]$ bounded by free surfaces is studied for $2<d<4$ in the limit $n\to \infty$. The self-consistent potential $V(z)$ which…