The very interesting magnetic properties of frustrated magnetic molecules are often hardly accessible due to the prohibitive size of the related Hilbert spaces. The finite-temperature Lanczos method is able to treat spin systems for Hilbert space sizes up to 10 9. Here we first demonstrate for exactly solvable systems that the method is indeed accurate. Then we discuss the thermal properties of one of the biggest magnetic molecules synthesized to date, the icosidodecahedron with antiferromagnetically coupled spins of s=1/2. We show how genuine quantum features such as the magnetization plateau behave as a function of temperature. Copyright EDP Sciences, SIF, Springer-Verlag Berlin Heidelberg 2010
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