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arXiv:1009.1712 · Acta Physica Polonica A

Effect of On-Site Coulomb Repulsion on Phase Transitions in Exactly Solved Spin-Electron Model

Lucia Gálisová, Jozef Strečka, Akinori Tanaka, Taras Verkholyak

Published Nov 1, 2010• 6 citations
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Abstract

A hybrid lattice-statistical model on doubly decorated planar lattices, which have localized Ising spins at their nodal lattice sites and two itinerant electrons at each pair of decorating sites, is exactly solved by the use of a generalized decoration-iteration transformation.Our main attention is focused on an influence of the on-site Coulomb repulsion on ground-state properties and critical behavior of the investigated system.

DOI
10.12693/aphyspola.118.942

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A hybrid lattice-statistical model on doubly decorated planar lattices, which have localized Ising spins at their nodal lattice sites and two itinerant electrons at each pair of decorating sites, is exactly solved by the use of a generalized decoration-iteration transformation.Our main attention is focused on an influence of the on-site Coulomb repulsion on ground-state properties and critical behavior of the investigated system.
A hybrid lattice-statistical model of doubly decorated two-dimensional lattices, which have localized Ising spins at its nodal sites and itinerant electrons delocalized over decorating sites, is exactly solved with the help of a generalized decoration-iteration transformation. Under the assumption of a quarter filling of each couple of the decorating sites, the ground state constitutes either spontaneously long-range ordered ferromagnetic or ferrimagnetic phase in dependence on whether the ferromagnetic or antiferromagnetic interaction between the localized Ising spins and itinerant electrons is considered. The critical temperature of the spontaneously long-range ordered phases monotonically increases upon strengthening the ratio between the kinetic term and the Ising-type exchange interaction.
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 (ρ ⁣= ⁣1ρ\!=\!1ρ=1) and a half (ρ ⁣= ⁣2ρ\!=\!2ρ=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 (ttt), the Ising coupling between the localized spins (J′J'J′), the electrostatic potential (VVV) and the electron concentration (ρρρ). In addition, it is detected that the increasing electrostatic potential has a reduction effect upon the deviation between critical temperatures in both statistical ensembles.
Phase transitions of the mixed spin-1/2 and spin-1 Ising-Heisenberg model on several decorated planar lattices consisting of interconnected diamonds are investigated within the framework of the generalized decoration-iteration transformation. The main attention is paid to the systematic study of the finite-temperature phase diagrams in dependence on the lattice topology. The critical behaviour of the hybrid quantum-classical Ising-Heisenberg model is compared with the relevant behaviour of its semi-classical Ising analogue. It is shown that both models on diamond-like decorated planar lattices exhibit a striking critical behaviour including reentrant phase transitions. The higher the lattice coordination number is, the more pronounced reentrance may be detected.
Ground-state and finite-temperature behaviour of the mixed spin-1/2 and spin-1 Ising–Heisenberg model on decorated planar lattices consisting of inter-connected diamonds is investigated by means of the generalised decoration–iteration mapping transformation. The obtained exact results clearly point out that this model has a rather complex ground state composed of two unusual quantum phases, which is valid regardless of the lattice topology as well as the spatial dimensionality of the investigated system. It is shown that the diamond-like decorated planar lattices with a sufficiently high coordination number may exhibit a striking critical behaviour including reentrant phase transitions with two or three consecutive critical points.