2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/53938Fisher's phenomenological renormalization method is used to calculate the mass gap and the correlation length of the $O(N)$ nonlinear $σ$ model on a semi-compact space $S^{1}\times {\bf R}^{2}$. This shows that the ultraviolet momentum cut-off does not conflict with the infrared cut-off along the $S^{1}$ direction. The mass gap on $S^{2}\times {\bf R}$ is also discussed.7 pagesHigh Energy Physics - Theorytext