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

Abstract

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

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Cited by in corpus (4)

• Ground-state and thermodynamic properties of the spin-$\frac{1}{2}$ Heisenberg model on the anisotropic triangular lattice
• High temperature series expansions of S = 1/2 Heisenberg spin models: algorithm to include the magnetic field with optimized complexity
• Finite-temperature phase transitions in $S=1/2$ three-dimensional Heisenberg magnets from high-temperature series expansions
• Derivation of the free energy, entropy and specific heat for planar Ising models: Application to Archimedean lattices and their duals