Phase transitions in the spinless Falicov-Kimball model with correlated hopping

TL;DR

This study uses Monte Carlo simulations to analyze phase transitions in the two-dimensional Falicov-Kimball model with correlated hopping, revealing different transition orders and the effects of correlated hopping on critical temperatures.

Contribution

It provides new insights into how correlated hopping influences phase stability and transition types in the Falicov-Kimball model.

Findings

All three phases persist up to the critical temperature.

Transition is first order for chessboard and striped phases, second order for segregated phase.

Correlated hopping amplitude affects critical temperature differently across phases.

Abstract

The canonical Monte-Carlo is used to study the phase transitions from the low-temperature ordered phase to the high-temperature disordered phase in the two-dimensional Falicov-Kimball model with correlated hopping. As the low-temperature ordered phase we consider the chessboard phase, the axial striped phase and the segregated phase. It is shown that all three phases persist also at finite temperatures (up to the critical temperature $\tau_c$) and that the phase transition at the critical point is of the first order for the chessboard and axial striped phase and of the second order for the segregated phase. In addition, it is found that the critical temperature is reduced with the increasing amplitude of correlated hopping $t'$ in the chessboard phase and it is strongly enhanced by $t'$ in the axial striped and segregated phase.