Characteristic values of the integral equation satisfied by the Mathieu functions and its application to a system with chirality-pair interaction on a one-dimensional lattice

We investigate low-temperature behaviors of a system with chirality-pair interaction on a one-dimensional lattice. In the course of the investigation, we evaluate asymptotic forms of the characteristic values of the integral equation satisfied by the Mathieu functions. It turns out that the low-temperature behavior of correlation length of the chirality-pair correlation function is different from the one for the Ising model of spin ±1 but akin to the one for the Ising model of infinite spin.