Localized fermions on the triangular lattice with Ising-like interactions

TL;DR

This paper investigates localized fermions on a triangular lattice with Ising-like interactions using Monte Carlo simulations, revealing phase diagrams and transition types depending on interaction signs and parameters.

Contribution

It provides a comprehensive analysis of phase transitions and magnetic ordering in a generalized extended Hubbard model with Ising interactions on a triangular lattice.

Findings

Ferromagnetic phase stable up to high temperatures for J<0.

First- and second-order phase transitions identified depending on parameters.

Antiferromagnetic order occurs for J>0 within specific U/|J| ranges.

Abstract

The model of localized fermions on the triangular lattice is analyzed in means of the Monte Carlo simulations in the grand canonical ensemble. The Hamiltonian of the system has a form of the extended Hubbard model (at the atomic limit) with nearest-neighbor Ising-like magnetic $J$ interactions and onsite Coulomb $U$ interactions. The model is investigated for both signs of $J$, arbitrary $U$ interaction and arbitrary chemical potential $\mu$ (or, equivalently, arbitrary particle concentration $n$). Based on the specific heat capacity and sublattice magnetization analyses, the phase diagrams of the model are determined. For ferromagnetic case ($J<0$), the transition from the ordered phase (which is a standard ferromagnet and can be stable up to $k_{B}T/|J| \approx 0.61$) is found to be second-order (for sufficiently large temperatures $k_{B}T/|J| \gtrsim 0.2$) or first-order (for $-1<U/|J|<-0.65$ at the half-filling, i.e., $n=1$). In the case of $J>0$, the ordered phase occurs in a range of $-1/2<U/|J|<0$ (for $n=1$), while for larger $U$ the state with short-range order is also found (also for $n \neq 1$). The ordered phase is characterized by an antiferromagnetic arrangement of magnetic moments in two sublattices forming the hexagonal lattice. The transition from this ordered phase, which is found also for $\mu \neq 0$ ($n \neq 1$) and $U/|J|>-1/2$ is always second-order for any model parameters. The ordered phase for $J>0$ can be stable up to $k_{B}T/|J| \approx 0.06$.