外磁场中二维伊辛模型的近似热力学
Approximate thermodynamics of the two-dimensional Ising model in an external magnetic field
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中文总结 AI 辅助
研究外磁场中二维伊辛模型的热力学，通过四元数表示应用小角度近似简化转移矩阵，得到自由能等热力学量的近似表达式，与数值模拟比较，在近似有效区域二者结果相符。
中文摘要 AI 辅助
我们引入了外磁场中二维伊辛模型热力学的近似表达式。外场打破了系统对称性，使自由能的精确计算复杂化。为此，我们将模型用四元数表示，对参考系应用小角度近似。该近似将转移矩阵简化为中心对称矩阵，其最大特征值已知且依赖于外场强度。我们据此写出系统自由能的近似表达式，并推导了磁化强度、磁化率、内能和比热。这些结果与用BKL算法进行的数值模拟作了比较。我们发现在近似有效的区域，近似表达式与数值模拟结果相符。
英文摘要
We introduce approximate expressions for the thermodynamics of the two-dimensional Ising model in an external magnetic field. The external field breaks the system's symmetry, which complicates the exact calculation of the free energy. To address this, we write the model in its quaternion representation to apply a small angle approximation with respect to a reference frame. The approximation simplifies the transfer matrix to a centrosymmetric matrix for which the largest eigenvalue is known and depends on the external field strength. We therefore write an approximate expression for the system's free energy and derive the magnetization, susceptibility, internal energy, and specific heat. These results are compared with numerical simulations performed with the BKL algorithm. We find that the approximate expressions and numerical simulations agree in regions where the approximation is valid.
