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

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. IntroductionExactly soluble lattice-statistical models attract scientific interest as they offer a valuable insight into diverse aspects of cooperative phenomena [1]. The mapping technique based on generalized algebraic transformations [2] belongs to the simplest mathematical methods, which allow us to obtain the exact solution for various statistical models. Recently, this approach has been applied to an interesting diamond-chain model of interacting spin-electron system [3]. This motivated us to start studying a similar spin-electron system on doubly decorated two-dimensional (2D) lattices in order to provide a deeper insight into how the mobile electrons influence their magnetic properties [4]. The investigated model system might provide guidance on a magnetic behavior of magnetic metals such as SrCo 6 O 11 [5], which contain both localized spins and itinerant electrons.2. Model and its exact solution Consider a hybrid lattice-statistical model of interacting spin-electron system on doubly decorated 2D lattices (see Fig. 1 in Ref. [4]), which have one localized Ising spin at each nodal lattice site and two delocalized mobile electrons at each couple of decorating sites. The total Hamiltonian of the model can be written as a sum over bond HamiltoniansĤ = kĤ k , where each bond HamiltonianĤ k involves all interaction terms of k-th couple of delocalized electronŝ

Magnetization processes and existence of reentrant phase transitions in coupled spin-electron model on doubly decorated planar lattices

“…In this concept an arbi-trary statistical-mechanical system, which merely interacts either with two or three outer Ising spins, may be replaced with effective interactions between the outer Ising spins through the generalized decoration-iteration or star-triangle mapping transformations [18][19][20]. This procedure was successfully applied to simulate magnetic properties of various two-component spin-electron systems in one [21][22][23][24][25][26] or two dimensions [27][28][29][30][31] with a good qualitative coincidence of magnetic behavior in real materials. For example, a 2D coupled spinelectron model could be used as a simplified theoretical model of selected rare-earth compounds, manganites or intermetallics with a quasi-2D character in which the existence of metamagnetic or reentrant transitions was observed [32][33][34][35].…”

Reentrant phase transitions of a coupled spin-electron model on doubly decorated planar lattices with two or three consecutive critical points

“…Following Fisher's ideas [33], an arbitrary statistical-mechanical system (even of quantum nature), which merely interacts with either two or three outer Ising spins, may be replaced with the effective interactions between the outer Ising spins through the generalized decoration-iteration or startriangle mapping transformations [33,34]. The procedure elaborated by Pereira et al [31,32] has been later adopted to other interacting spin-electron models in one [35][36][37][38][39][40][41][42] or two dimensions [43][44][45][46]. The interest in this field of study has two different reasons.…”

Direct algebraic mapping transformation for decorated spin models

“…Another interesting application of decoration transformation was also investigated in a work by Pereira et al [38] in which they considered a delocalized interstitial electrons on a diamond-like chain and also investigated the magnetocaloric effect in a kinetically frustrated diamond chain [39]. Meanwhile, Strecka et al [32] discussed the localized Ising spins and itinerant electrons in two-dimensional models, as well as two-dimensional spin-electron models with coulomb repulsion [33]. Recently, the decoration transformation approach has also been applied to spinless interacting particles, thus showing the possibility of application to interacting electron models [40].…”