We investigate the thermodynamics of a one-dimensional Hubbard model with bond-charge interaction X using the transfer-matrix renormalization-group method. Numerical results for various quantities such as spin and charge susceptibilities, particle densities, specific heat, and thermal correlation lengths are presented and discussed. We compare our data also to results for the exactly solvable case
X/t=1 as well as to bosonization results for weak coupling $X/t\ensuremath{\ll}1,$ which shows excellent agreement. We confirm the existence of a Tomonaga-Luttinger and a Luther-Emery liquid phase, in agreement with previous studies at zero temperature. Thermal singlet-pair-correlation lengths are shown to dominate density and spin correlations for finite temperatures in certain parameter regimes.
A semi-phenomenological theory is developed on the basis of some assumptions in order to study the singularities of thermodynamic quantities in the vicinity of the Curie point. First, microscopic expressions are found for the coefficients in the expansion of the thermodynamic potential in terms of cumulants. Cumulants of all order are calculated in the one-dimensional Ising model, and the series expansion of the fourth order cumulant is also obtained in the two-dimensional Ising model. The three-dimensional Heisenberg model is also discussed, using the result of Rushbrooke et al. In all cases, the fourth order coefficient in the expansion of the thermodynamic potential tends to zero at the Curie points. And, in the last case, the eighth order coefficient diverges at the Curie point.