The long-distance asymptotic for the correlation function of the third spin components in the XX0 model with the interaction of four neighboring sites

The XX0 model in an external magnetic field directed along the $z$-axis is discussed. The Hamiltonian describing exchange interaction in two and four neighboring sites of a chain is constructed. An integral representation for the equal-time temperature correlation function of the third spin components is presented. The correlation radius from the long-distance asymptotic of this correlation function is calculated and its low-temperature behavior is studied.