Thermodynamic properties of the dimerized and frustrated $S=1/2\mathrm{}$ chain

By high-temperature series expansion, exact diagonalization, and temperature density-matrix renormalization the magnetic susceptibility $\chi \mathrm{}\left(T\right)\mathrm{}$ and the specific heat $C\left(T\right)\mathrm{}$ of dimerized and frustrated $S=1/2\mathrm{}$ chains are computed. All three methods yield reliable results, in particular, for not too small temperatures or not too small gaps. The series-expansion results are provided in the form of polynomials allowing very fast and convenient fits in data analysis using algebraic programs. We discuss the difficulty to extract more than two coupling constants from the temperature dependence of $\chi \mathrm{}\left(T\right).$