We present a method to compute the magnetic susceptibility of spin systems at all temperatures in one and two dimensions. It relies on an approximation of the entropy versus energy (microcanonical potential function) on the whole range of energies. T
he intrinsic constraints on the entropy function and a careful treatment of boundary behaviors allow to extend the standard high temperature series expansions (HTE) towards zero temperature, overcoming the divergence of truncated HTE. This method is benchmarked against two one-dimensional solvable models: the Ising model in longitudinal field and the XY model in a transverse field. With ten terms in the HTE, we find a spin susceptibility within a few % of the exact results in the whole range of temperature. The method is then applied to two two-dimensional models: the supposed-to-be gapped Heisenberg model and the $J_1$-$J_2$-$J_d$ model on the kagome lattice.
We have obtained the zero-temperature phase diagram of the kagome antiferromagnet with Dzyaloshinskii-Moriya interactions in Schwinger-boson mean-field theory. We find quantum phase transitions (first or second order) between different topological sp
in liquids and Neel ordered phases (either the $sqrt{3} times sqrt{3}$ state or the so-called Q=0 state). In the regime of small Schwinger-boson density, the results bear some resemblances with exact diagonalization results and we briefly discuss some issues of the mean-field treatment. We calculate the equal-time structure factor (and its angular average to allow for a direct comparison with experiments on powder samples), which extends earlier work on the classical kagome to the quantum regime. We also discuss the dynamical structure factors of the topological spin liquid and the Neel ordered phase.
