Some Properties of Two-Dimensional Extended Repulsive Hubbard Model with Intersite Magnetic Interactions - A~Monte Carlo Study

Abstract

In this paper the two dimensional extended Hubbard model with intersite magnetic Ising-like interaction in the atomic limit is analyzed by means of the classical Monte Carlo method in the grand canonical ensemble. Such an effective simple model could describe behavior of insulating (anti)ferromagnets. In the model considered the Coulomb interaction (U ) is on-site and the magnetic interactions in z-direction (J > 0, antiferromagnetic) are restricted to nearest-neighbors. Simulations of the model have been performed on a square lattice consisting of N = L × L = 400 sites (L = 20) in order to obtain the full phase diagram for U/(4J) = 1. Results obtained for on-site repulsion (U > 0) show that, apart from homogeneous non-ordered (NO) and ordered magnetic (antiferromagnetic, AF) phases, there is also a region of phase separation (PS: AF/NO) occurrence. We present a phase diagram as well as some thermodynamic properties of the model for the case of U/(4J) = 1 (and arbitrary chemical potential and arbitrary electron concentration). The AF-NO transition can be second-order as well as first-order and the tricritical point occurs on the diagram. PACS numbers: 71.10.Fd -Lattice fermion models (Hubbard model, etc.), 75.10.-b -General theory and models of magnetic ordering, 75.30.Fv -Spin-density waves, 64.75.Gh -Phase separation and segregation in model systems (hard spheres, Lennard-Jones, etc.), 71.10.Hf -Non-Fermi-liquid ground states, electron phase diagrams and phase transitions in model systems

Monte Carlo Study of Phase Separation in Magnetic Insulators

“…They differ if the AF-NO transition is first-order. Details of this method can be found in [14]. With simulations done for fixedμ and k B T /4J vs.μ/4J, it is possible to obtain phase diagrams as a function of n (shown in Fig.…”

“…chemical potential dependence of electron concentration curvesn(µ). The Monte Carlo algorithm used in this analysis consists of three steps: (i) creation, (ii) destruction, and (iii) moving of particle, all of them with appropriate probability P ∼ exp (∆E/(k B T )) [11][12][13][14]. It is worth noting, that for constant values of concentration a simpler algorithm with only step (iii) -"move" would be sufficient.…”

“…Unfortunately, addition of chemical potential term in the Hamiltonian prevents us from implementing cluster updates algorithm, so only local updates [15] are used here. The details of the algorithm used can be found in [11][12][13][14].…”

“…Within the variational approach (with on-site U term treated exactly and mean field decoupling of intersite term J) the model has been analyzed for half-filing (n = 1) [21,22] as well as for arbitrary electron concentration 0 ≤ n ≤ 2 [23] (these results are rigorous in the limit of infinite dimensions d → +∞). Our preliminary Monte Carlo (MC) results have been presented in [13,14] for L = 10 and onsite repulsion: U/(4J) = 1, 10 (corresponding to rather weak and strong coupling, respectively) [13] as well as for L = 20 and U/(4J) = 1 [14].…”

Superconductivity, Metastability and Magnetic Field Induced Phase Separation in the Atomic Limit of the Penson-Kolb-Hubbard Model

“…The interplay and competition between superconductivity and intersite magnetic [24][25][26][27][28] or density-density [16,[29][30][31][32][33][34][35][36] interactions is a very interesting problem. Some results concerning the interplay of these interactions with the pair hopping term for B = 0 have been presented in [5,[37][38][39][40][41].…”