Low-temperature expansions and the Euler-Maclaurin formula

Thermodynamic quantities of solvable models such as one-dimensional Heisenberg model can be obtained through the finite temperature Baxter formula. For the low-temperature expansions, the estimate of the finite size corrections by use of the Euler-Maclaurin formula is essential. There has been a question on the convergence of such calculations. In this paper, choosing the XX model as a simple example, we show explicitly that the Euler-Maclaurin formula reproduces the correct low-temperature expansion of the free energy.