In this article, we study Planckian effects on statistical thermodynamic properties of one dimensional polarized Ising model with an external electric field. We introduce Planckian effects by rewriting the Lagrangian of a static electromagnetic field in terms of deformed operators to obtain the corrected Lagrangian for a static electric field, and then deduce the corrected static electric field. Then we write down the corrected Ising model Hamiltonian in terms of the corrected static electric field. Corrected quantities such as the mean energy, Helmholtz free energy, and entropy are derived using the corrected Ising model Hamiltonian. Also, corrected quantities such as the polarization, dielectric constant, and polarizability tensor are derived. The expressions for the upper bounds of the deformation parameter α and the minimal length are written in terms of the dielectric constant. Using some experimental inputs we obtain the upper bound on the minimal length.

中文翻译：

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外部电场中伊辛模型的普朗克效应

在本文中，我们研究了具有外部电场的一维极化伊辛模型的统计热力学性质的普朗克效应。我们引入普朗克效应，通过用变形算子重写静态电磁场的拉格朗日量，得到静态电场的校正拉格朗日量，然后推导出校正的静态电场。然后我们根据修正的静电场写出修正的伊辛模型哈密顿量。使用修正的伊辛模型哈密顿量导出修正量，例如平均能量、亥姆霍兹自由能和熵。此外，还导出了诸如极化、介电常数和极化率张量等校正量。变形参数上限的表达式α最小长度以介电常数表示。使用一些实验输入，我们获得了最小长度的上限。