Tenth-order high-temperature expansion for the susceptibility and the specific heat of spin-s Heisenberg models with arbitrary exchange patterns: Application to pyrochlore and kagome magnets

Abstract: We present the high-temperature expansion (HTE) up to 10th order of the specific heat C and the uniform susceptibility \chi for Heisenberg models with arbitrary exchange patterns and arbitrary spin quantum number s. We encode the algorithm in a C++ program which allows to get explicitly the HTE series for concrete Heisenberg models. We apply our algorithm to pyrochlore ferromagnets and kagome antiferromagnets using several Pad\'e approximants for the HTE series. For the pyrochlore ferromagnet we use the HTE data for \chi to estimate the Curie temperature T_c as a function of the spin quantum number s. We find that T_c is smaller than that for the simple cubic lattice, although both lattices have the same coordination number. For the kagome antiferromagnet the influence of the spin quantum number s on the susceptibility as a function of renormalized temperature T/s(s+1) is rather weak for temperatures down to T/s(s+1) \sim 0.3. On the other hand, the specific heat as a function of T/s(s+1) noticeably depends on s. The characteristic maximum in C(T) is monotonously shifted to lower values of T/s(s+1) when increasing s.