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We present a study of the low temperature phases of the antiferromagneticextended classical Heisenberg model in the kagome lattice, up to third nearestneighbors. First, we focus on the degenerate lines in the boundaries of thewell-known staggered chiral phases. These boundaries have either semi-extensiveor extensive degeneracy, and we discuss the partial selection of states bythermal fluctuations. Then, we study the model under an external magnetic fieldon these lines and in the staggered chiral phases. We pay particular attentionto the highly frustrated point, where the three exchange couplings are equal.We show that this point can me mapped to a model with spin liquid behavior andnon-zero chirality. Finally, we explore the effect of Dzyaloshinskii-Moriya(DM) interactions in two ways: an homogeneous and a staggered DM interaction.In both cases, there is a rich low temperature phase diagram, with differentspontaneously broken symmetries and non trivial chiral phases.

Degenerate and chiral states in the extended Heisenberg model in the kagome lattice