Comparative Study of a Critical Behavior of a Coupled Spin-Electron Model on a Doubly Decorated Square Lattice in the Canonical and Grand-Canonical Ensemble

TL;DR

This paper investigates the critical behavior of a hybrid spin-electron model on a decorated square lattice, analyzing how critical temperature varies with parameters and ensemble type at specific electron fillings.

Contribution

It provides a rigorous comparison of critical temperatures in canonical and grand-canonical ensembles for a coupled spin-electron model, highlighting parameter sensitivities.

Findings

Critical temperature differs significantly between ensembles.

Electrostatic potential reduces the difference in critical temperatures.

Critical temperature is highly sensitive to model parameters.

Abstract

The critical behavior of a hybrid spin-electron model with localized Ising spins placed on nodal sites and mobile electrons delocalized over bonds between two nodal lattice sites is analyzed by the use of a generalized decoration-iteration transformation. Our attention is primarily concentrated on a rigorous analysis of a critical temperature in canonical and grand-canonical statistical ensemble at two particular electron concentrations, corresponding to a quarter ($\rho\!=\!1$) and a half ($\rho\!=\!2$) filled case. It is found that the critical temperature of the investigated spin-electron system in the canonical and grand-canonical ensemble may be remarkably different and is very sensitive to the competition among the model parameters like the electron hopping amplitude ($t$), the Ising coupling between the localized spins ($J'$), the electrostatic potential ($V$) and the electron concentration ($\rho$). In addition, it is detected that the increasing electrostatic potential has a reduction effect upon the deviation between critical temperatures in both statistical ensembles.