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We present an interpolation method for the specific heat $c_v(T)$, when thereis a phase transition with a logarithmic singularity in $c_v$ at a criticaltemperature $T=T_c$. The method uses the fact that $c_v$ is constrained both byits high temperature series expansion, and just above $T_c$ by the type ofsingularity. We test our method on the ferro and antiferromagnetic Ising modelon the two-dimensional square, triangular, honeycomb, and kagome lattices,where we find an excellent agreement with the exact solutions. We then explorethe XXZ Heisenberg model, for which no exact results are available.

Logarithmic divergent specific heat from high-temperature series expansions: application to the two-dimensional XXZ Heisenberg model