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We present a method to compute the magnetic susceptibility of spin systems atall temperatures in one and two dimensions. It relies on an approximation ofthe entropy versus energy (microcanonical potential function) on the wholerange of energies. The intrinsic constraints on the entropy function and acareful treatment of boundary behaviors allow to extend the standard hightemperature series expansions (HTE) towards zero temperature, overcoming thedivergence of truncated HTE. This method is benchmarked against twoone-dimensional solvable models: the Ising model in longitudinal field and theXY model in a transverse field. With ten terms in the HTE, we find a spinsusceptibility within a few \% of the exact results in the whole range oftemperature. The method is then applied to two two-dimensional models: thesupposed-to-be gapped Heisenberg model and the $J_1$-$J_2$-$J_d$ model on thekagome lattice.

Spin susceptibility of quantum magnets from high to low temperatures