Abstract. An elementary proof is given that the statistical mechanical transfer matrix, when symmetric, has a maximum eigenvalue which is non-degenerate and larger than the absolute value of any other eigenvalue. Moreover, the corresponding eigenvector can be chosen so that all its entire entries are strictly positive.

A corrigendum for this article has been published in 1977 J. Phys. A: Math. Gen. 10 1259

Print publication: Issue 8 (August 1976)