Planckian effects on Ising model in an external electric field

Abstract

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.