The thermodynamics of the spin-$S$ anisotropic quantum $XXZ$ chain witharbitrary value of $S$ and unitary norm, in the high-temperature regime, isreported. The single-ion anisotropy term and the interaction with an externalmagnetic field in the $z$-direction are taken into account. We obtain, forarbitrary value of $S$, the $\beta$-expansion of the Helmholtz free energy ofthe model up to order $\beta^6$ and show that it actually depends on$\frac{1}{S(S+1)}$. Its classical limit is obtained by simply taking $S\to\infty$. At $h=0$ and D=0, our high temperature expansion of the classicalmodel coincides with Joyce's exact solution\cite{joyce_prl}. We study, in thehigh temperature region, some thermodynamic quantities such as the specificheat and the magnetic susceptibility as functions of spin and verify for whichvalues of $S$ those thermodynamic functions behave classically. Their finitetemperature behavior is inferred from interpolation of their high- andlow-temperature behavior, and shown to be in good agreement with numericalresults. The finite temperature behavior is shown for higher values of spin.
展开▼
机译：报告了在高温状态下具有任意值S $和统一范数的自旋S $ S $各向异性量子$ XXZ $链的热力学。考虑了单离子各向异性项以及在$ z $方向上与外部磁场的相互作用。我们获得$ S $的任意值，模型的Helmholtz自由能的$ \ beta $展开直至订购$ \ beta ^ 6 $，并证明它实际上取决于$ \ frac {1} {S（S +1）} $。它的经典极限是通过简单地将$ S \ to \ infty $来获得的。在$ h = 0 $和D = 0时，我们经典模型的高温膨胀与Joyce的精确解\ cite {joyce_prl}一致。我们在高温区域研究了一些热力学量（例如比热和磁化率）作为自旋函数，并验证了这些热力学函数对于$ S $的哪个值表现经典。从高温和低温行为的插值可以推断出它们的有限温度行为，并与数值结果非常吻合。对于较高的自旋值，显示了有限的温度行为。
展开▼
