The prohibition of finite-temperature phase transition in one-dimensional (1D) Ising models and 1D/2D quantum Heisenberg models with short-range interactions fundamentally constrains the application potentials of low-dimensional magnetic materials. Recently, ultranarrow phase crossover (UNPC), which can approach a transition at a desirable finite temperature $T_0$ 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 prohibition of finite-temperature phase transition in one-dimensional (1D) Ising models and 1D/2D quantum Heisenberg models with short-range interactions fundamentally constrains the application potentials of low-dimensional magnetic materials. Recently, ultranarrow phase crossover (UNPC), which can approach a transition at a desirable finite temperature $T_0$ 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.

cond-mat.str-elCross-listedarXiv:2511.06442Nov 11, 20250 citations

Phase diagram of the Heisenberg model on the decorated honeycomb lattice.

Dmitrii Kochkov, Rebecca Flint, Bryan K. Clark

Bulletin of the American Physical SocietyMar 17, 20170 citations

Disordered phase of a two-dimensional Heisenberg model with

S. Moukouri

arXiv:cond-mat/0510288Physics Letters ANov 30, 200514 citations

A possible coexistence of spontaneous magnetic order and thermal entanglement in a spin-1/2 Ising–Heisenberg diamond-decorated square lattice

Azadeh Ghannadan, Jozef Strečka

The spin-1/2 Ising-Heisenberg model on a diamond-decorated square lattice is exactly solved by the decoration-iteration transformation, which establishes an exact mapping correspondence with the spin-1/2 Ising model on a square lattice with an effective temperature-dependent interaction between the nearest-neighbor spins. Exact results for the pair correlation function and spontaneous magnetization of the Heisenberg spins gained from the exact mapping equivalence allow a straightforward implementation of the concurrence, which may serve as a measure of the bipartite entanglement within decorating Heisenberg spin pairs. It is evidenced that the concurrence gradually diminishes upon increase of temperature above a disordered monomer-dimer ground state until it completely vanishes at a threshold temperature, while the concurrence is either always zero above a spontaneously ordered ferrimagnetic ground state or it shows a peculiar thermally assisted reentrance accompanied with a mutual coexistence of the spontaneous ferrimagnetic long-range order and the thermal entanglement.The spin-1/2 Ising-Heisenberg model on a diamond-decorated square lattice is exactly solved by the decoration-iteration transformation, which establishes an exact mapping correspondence with the spin-1/2 Ising model on a square lattice with an effective temperature-dependent interaction between the nearest-neighbor spins. Exact results for the pair correlation function and spontaneous magnetization of the Heisenberg spins gained from the exact mapping equivalence allow a straightforward implementation of the concurrence, which may serve as a measure of the bipartite entanglement within decorating Heisenberg spin pairs. It is evidenced that the concurrence gradually diminishes upon increase of temperature above a disordered monomer-dimer ground state until it completely vanishes at a threshold temperature, while the concurrence is either always zero above a spontaneously ordered ferrimagnetic ground state or it shows a peculiar thermally assisted reentrance accompanied with a mutual coexistence of the spontaneous ferrimagnetic long-range order and the thermal entanglement.

Chinese Journal of PhysicsJan 13, 20244 citations

Axial decorated Ising model with competing interaction

Roberto J. V. dos Santos, S. Coutinho, J. R. L. de Almeida

The phase diagram and the thermodynamics of the axial decorated Ising model on a square lattice with m-dimensional bond spins are studied for the m=1 (Ising), m=2 (XY), m=3 (Heisenberg) and m= infinity cases. Competing interactions between the site and decorating bond spins have been considered. The expressions for the partition function, the thermodynamics and the pair correlation functions of the decorated Ising chain have been analytically obtained. The effect of the dimensionality of the decorating bond spin on the thermodynamic behaviour of both models is analyzed.The phase diagram and the thermodynamics of the axial decorated Ising model on a square lattice with m-dimensional bond spins are studied for the m=1 (Ising), m=2 (XY), m=3 (Heisenberg) and m= infinity cases. Competing interactions between the site and decorating bond spins have been considered. The expressions for the partition function, the thermodynamics and the pair correlation functions of the decorated Ising chain have been analytically obtained. The effect of the dimensionality of the decorating bond spin on the thermodynamic behaviour of both models is analyzed.

Journal of Physics A Mathematical and GeneralOct 21, 198612 citations

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.