Finite-size Analysis of $O(N)$ Nonlinear $\sigma$ Model on Semi-compact Spaces

Abstract

Fisher's phenomenological renormalization method is used to calculate the mass gap and the correlation length of the $O(N)$ nonlinear $\sigma$ model on a semi-compact space $S^1\times {\mathbf{R}}^2$. 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 $S^2\times \mathbf{R}$ is also discussed.

7 pages