Low Temperature Expansions for One-Dimensional Heisenberg Model(一次元ハイゼンベルグ模型の低温展開)

M. J. Škrinjaŕ, D. Kapor, Jovan P. Šetrajčić

Hideyuki Mizuta, Miki Wadati

Thermodynamic quantities of solvable models such as one–dimensional Heisenberg model can be obtained through the Finite temperature Baxter formula. For the low–temperature expansions, the estimate of the finite size corrections by use of the Euler–Maclaurin formula is essential. There has been a question on the convergence of such calculations. In this paper, we confirm that the Euler–Maclaurin formula gives the correct low–temperature expansion of the free energy for the XXZ Heisenberg model.

Andreas Hehn, Natalija van Well, Matthias Troyer

Hideyuki Mizuta, Miki Wadati

Thermodynamic quantities of solvable models such as one–dimensional Heisenberg model can be obtained through the finite temperature Baxter formula. For the low–temperature expansions, the estimate of the finite size corrections by use of the Euler–Maclaurin formula is essential. There has been a question on the convergence of such calculations. In this paper, choosing the XX model as a simple example, we show explicitly that the Euler–Maclaurin formula reproduces the correct low–temperature expansion of the free energy.

Shan-Chang Tang

It is well known that KT transition in 2d XY model is driven by the binding and unbinding of topological defects, which can be characterized by the fluctuation of topological charges inside a region. We extend the idea into the 2d Heisenberg model and calculate the fluctuation through high-temperature and low-temperature expansion respectively. It is found that the fluctuation of topological charges is proportional to the area of the region at high temperatures while obeys the perimeter law at low temperatures.

Cyril Domb, David W. Wood