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arXiv:2008.12551 · Acta Physica Polonica A

Comparative Study of a Critical Behavior of a Coupled Spin-Electron Model on a Doubly Decorated Square Lattice in the Canonical and Grand-Canonical Ensemble

Hana Čenčariková, Natália Tomašovičová

Published May 1, 2020• 0 citations
arXivHTMLPDF

Abstract

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 ($ρ\!=\!1$) and a half ($ρ\!=\!2$) 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 ($t$), the Ising coupling between the localized spins ($J'$), the electrostatic potential ($V$) and the electron concentration ($ρ$). In addition, it is detected that the increasing electrostatic potential has a reduction effect upon the deviation between critical temperatures in both statistical ensembles.

DOI
10.12693/aphyspola.137.607

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•Sep 5, 2011•0 citations
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.
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 mixed-spin-(1∕2,SB,SC)(1∕2,{S}_{\mathrm{B}},{S}_{\mathrm{C}})(1∕2,SB​,SC​) Ising model on a decorated square lattice with two different kinds of decorating spins SB{S}_{\mathrm{B}}SB​ and SC{S}_{\mathrm{C}}SC​ $({S}_{\mathrm{B}}\ensuremath{\ne}{S}_{\mathrm{C}})$ placed on its horizontal and vertical bonds, respectively, is exactly solved by establishing a precise mapping relationship with the corresponding spin-1∕21∕21∕2 Ising model on an anisotropic square (rectangular) lattice. The effect of uniaxial single-ion anisotropy acting on both types of decorating spins SB{S}_{\mathrm{B}}SB​ and SC{S}_{\mathrm{C}}SC​ is examined, in particular. If decorating spins SB{S}_{\mathrm{B}}SB​ and SC{S}_{\mathrm{C}}SC​ are integer and half-odd-integer, respectively, or if the reverse is the case, the model under investigation displays a very peculiar critical behavior that had bearing on the spontaneously ordered ``quasi-one-dimensional'' spin system, which appears as a result of the single-ion anisotropy strengthening. We have found convincing evidence that this remarkable spontaneous ordering virtually arises even though all integer-valued decorating spins tend toward their ``nonmagnetic'' spin state S=0S=0S=0 and the system becomes disordered only upon further increase of the single-ion anisotropy. The single-ion anisotropy parameter is also at an origin of various temperature dependences of the total magnetization when imposing the pure ferrimagnetic or the mixed ferro-ferrimagnetic character of the spin arrangement.
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.
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 μ (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|≈0.61) is found to be second order (for sufficiently large temperatures k_{B}T/|J|≳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≠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 μ≠0 (n≠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|≈0.06.
Magnetoelastic properties of the spin-1/2 Ising-Heisenberg model on doubly decorated planar lattices partially amenable to lattice vibrations are examined within the framework of the harmonic approximation and decoration-iteration transformation. It is shown that the mutual interplay between quantum spin fluctuations and local fluctuations of lattice spacings enhances typical quantum features like the quantum reduction of the magnetization in the ground state of the quantum antiferromagnetic phase, while it does not affect the ground-state behaviour of the classical ferromagnetic phase by no means. It also turns out that local fluctuations of lattice spacings are responsible for a much more pronounced reduction of the critical temperature in the quantum antiferromagnetic phase than in the classical ferromagnetic phase.