Correlation transitions in the Ising chain with competing short-range and long-range mirror interactions

We present exact four-spin- and string-correlation functions derived for an Ising chain with competing geometrical nearest-neighbor short-range and mirror-image-type long-range interactions. Unusual T not equal 0 correlation effects were found, indicating qualitative changes in the behavior of the system in different T domains. These domains are not separated by a sharp, traditional phase transition, but are delimited by a temperature T-i at which the exact connected four-spin-correlation function vanishes. At the same T-i the pair-correlation function changes its character: The functional form of the correlation length and the nature of the long-range decay are modified. [S1063-651X(98)09610-X].