arXiv:0908.2880 · Journal of Physics Conference Series

Phase transitions in exactly solvable decorated model of localized Ising spins and itinerant electrons

Jozef Strečka, A Tanaka, M Jaščur

Published Jan 1, 2010• 9 citations

Abstract

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.

DOI: 10.1088/1742-6596/200/2/022059

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arXiv:0908.2880 · Journal of Physics Conference Series

Phase transitions in exactly solvable decorated model of localized Ising spins and itinerant electrons

Jozef Strečka, A Tanaka, M Jaščur

Published Jan 1, 2010• 9 citations

arXiv HTML PDF

Abstract

DOI: 10.1088/1742-6596/200/2/022059

Related papers

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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.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.

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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.

T_0

arbitrarily closely, was discovered in 1D decorated Ising chains and ladders. Here we present a theoretical study of similarly decorated, yet much more challenging, quantum Heisenberg ferrimagnets in a magnetic field, which features ferromagnetic backbone exchange

J

, antiferromagnetic site-decoration coupling

J_{AF}

, and different magnetic moments for the backbone and decorating spins

μ_aS_a<μ_bS_b

. We exactly solved the model in the large

J

limit -- as a central-macrospin model -- and found two finite-temperature second-order transitions; just above

T_{c2}

a ``half-ice, half-fire'' regime appears. Finite-

J

weak-field results follow from an effective-field mapping, suggesting the emergence of UNPC at finite

T_0

in 2D square lattices thanks to its exponentially strong initial magnetic susceptibility

χ_0\propto e^{4πS_a^2 J/T_0}

, though less likely in 1D chains where

χ_0\propto J/T_0

. These results may shed light on new technological applications of low-dimensional quantum spin systems and attract experimental and computational tests.

The mixed-spin-

(1∕2,{S}_{\mathrm{B}},{S}_{\mathrm{C}})

Ising model on a decorated square lattice with two different kinds of decorating spins

{S}_{\mathrm{B}}

and

{S}_{\mathrm{C}}

$({S}_{\mathrm{B}}\ensuremath{\ne}{S}_{\mathrm{C}})$ placed on its horizontal and vertical bonds, respectively, is exactly solved by establishing a precise mapping relationship with the corresponding spin-

1∕2

Ising model on an anisotropic square (rectangular) lattice. The effect of uniaxial single-ion anisotropy acting on both types of decorating spins

{S}_{\mathrm{B}}

and

{S}_{\mathrm{C}}

is examined, in particular. If decorating spins

{S}_{\mathrm{B}}

and

{S}_{\mathrm{C}}

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=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.