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 models 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.

Ground-state and thermodynamic properties of the spin-$\frac{1}{2}$ Heisenberg model on the anisotropic triangular lattice

“…However, it has been suggested that e 0 can be obtained selfconsistently by maximizing the number of coinciding Padé approximants (CPAs). This criteria has recently proven to give good results in several cases [44][45][46].…”

“…Several interpolation methods have been proposed to overcome this limitation of the HTSE [41][42][43][44][45][46]. In particular, in the absence of finite-temperature phase transitions, the so-called Figure 1: Spatially anisotropic triangular lattice, with J exchange interaction running along two directions (purple) and J running along the remaining one (green).…”

“…The main problem of the method is that it depends on the knowledge of the lowtemperature behavior of the specific heat and the ground-state energy which is not usually available for quantum models. Nonetheless, looking for the highest number of coinciding Padé approximants has proven to be a way to narrow down the parameter space, allowing to obtain certain parameters self-consistently [44][45][46].…”