Abstract: Domains with a transitional dimension are very interesting in the research of finite-size effects.This paper investigates the finite-size effects of a infinite long cylindrical system in 3 dimensions which is a domain between 2 dimensions and 3 dimensions,studies this problem by using an O(n)-symmetrical φ~4 field model and gets the exact solation when n→∞,gives the exact expressions of magnetic susceptibility and specific heat capacity to this cylindrical system.These results can be used to study the finit...