论文标题
一维自旋一晶石模型的热力学几何形状
Thermodynamic geometry of one-dimensional spin one lattice models
论文作者
论文摘要
对于各种参数制度（包括Blume-Capel限制和Griffiths模型限制），研究了一维的Blume Emery Griffith模型和相关的标量曲率（S），获得了状态空间几何形状。对于一维情况，发现了两个互补的几何形状及其相关曲率$ r_m $和$ r_q $的$ r_q $，与两个阶参数中的波动有关，即磁矩和四极力矩。在两个曲率和两个相应的相关长度$ξ_1$和$ξ_2$之间的参数空间的重要区域中获得了一个出色的协议。还发现三维标量曲率$ r_g $有效地编码交互。通过利用Ruppeiner的猜想，将奇异自由能与热力学标量曲率相关的逆向来获得，从临界点附近的自由能的缩放函数和三智度点获得。
State space geometry is obtained for the one dimensional Blume Emery Griffiths model and the associated scalar curvature(s) investigated for various parameter regimes, including the Blume-Capel limit and the Griffiths model limit. For the one-dimensional case two complementary geometries with their associated curvatures $R_m$ and $R_q$ are found which are related to the fluctuations in the two order parameters, namely the magnetic moment and the quadrupole moment. An excellent agreement is obtained in significant regions of the parameter space between the two curvatures and the two corresponding correlation lengths $ξ_1$ and $ξ_2$. The three dimensional scalar curvature $R_g$ is also found to efficiently encode interactions. The scaling function for the free energy near critical points and the tricritical point is obtained by making use of Ruppeiner's conjecture relating the inverse of the singular free energy to the thermodynamic scalar curvature.
