Long-range and non-decaying Ising model mapping of effective interactions in multilayer graphene within a microcavity

Abstract

In this work, the effective interactions of $N$ graphene layers within a microcavity are analyzed using the Schrieffer–Wolff transformation. Considering the vacuum fluctuations of the cavity field, electrons in different layers get coupled through Heisenberg-type interactions. Applying a mean-field approximation for the ground state energy, we obtain the set of measurable parameters at which the free energy is minimum, and we analyze the critical parameters at which phase transitions occur, where we consider an initial configuration where electrons are randomly distributed in the valence and conduction band. In particular, different geometrical and dynamical configurations are considered, such as $N$ electrons with identical momentum and alternate momentum and alternate angles. The critical temperature as a function of the electron momentum angles and energies was obtained, showing a nontrivial dependence with the modes of oscillation. Finally, we discuss the critical temperature dependence with respect to the energy gap between electrons in different layers and for random angles.