Thermodynamic properties of the classical Heisenberg chain with nearest- and next-nearest-neighbor interactions

Exact results for the thermodynamic quantities of the one-dimensional classical Heisenberg model with nearest- and next-nearest-neighbor exchange interactions are obtained by means of the numerical transfer matrix method. For a wide range of exchange constants, the system exhibits helical short-range order on which we focus our attention. We find that the Fourier-transformed spin correlation function shows a maximum with asymmetric shape at the characteristic wave-number ±q_m (≠0, ±π). The correlation length defined as the inverse of the width at q=q_m obeys a simple scaling law and shows a power-law singularity at zero temperature. Results for the heat capacity and the susceptibility are also presented and discussed in connection with the helical short-range order.