Bernu B, Lhuillier C
LPTMC, UMR 7600 of CNRS, UPMC, Paris-Sorbonne, F-75252 Paris Cedex 05, France.
Phys Rev Lett. 2015 Feb 6;114(5):057201. doi: 10.1103/PhysRevLett.114.057201. Epub 2015 Feb 4.
We explain how and why all thermodynamic properties of spin systems can be computed in one and two dimensions in the whole range of temperatures overcoming the divergence towards zero temperature of the standard high-temperature series expansions (HTEs). The method relies on an approximation of the entropy versus energy (microcanonical potential function) on the whole range of energies. The success is related to the intrinsic physical constraints on the entropy function and a careful treatment of the boundary behaviors. This method is benchmarked against two one-dimensional solvable models: the Ising model in longitudinal field and the XY model in a transverse field. With ten terms in the HTE, we find a spin susceptibility within a few percent of the exact results over the entire range of temperatures. The method is then applied to two two-dimensional models: the supposedly gapped Heisenberg model and the J(1)-J(2)-J(d) model on the kagome lattice.
我们解释了如何以及为何在整个温度范围内，能够在一维和二维中计算自旋系统的所有热力学性质，克服了标准高温级数展开（HTEs）在趋近于零温度时的发散问题。该方法依赖于在整个能量范围内对熵与能量（微正则势函数）的近似。成功的关键在于熵函数的内在物理约束以及对边界行为的仔细处理。此方法以两个一维可解模型为基准进行测试：纵向场中的伊辛模型和横向场中的XY模型。通过HTEs中的十项，我们在整个温度范围内得到的自旋磁化率与精确结果相差在百分之几以内。然后该方法被应用于两个二维模型：推测具有能隙的海森堡模型和 kagome 晶格上的J(1)-J(2)-J(d)模型。
