The magnetic and thermodynamic properties of a ferrimagnetic decorated spin- $(\frac{1}{2},1)$ Heisenberg chain with spin-1 pendant spins are investigated for three cases: (A) ${J}_{1},{J}_{2}>0$ ; (B) ${J}_{1}>0$ and ${J}_{2}<0$ ; and (C) ${J}_{1}<0$ and ${J}_{2}>0$ , where ${J}_{1}$ and ${J}_{2}$ are the exchange couplings between spins in the chain and along the rung, respectively. The low-lying and magnetic properties are explored jointly by the real-space renormalization group, spin wave, and density-matrix renormalization-group methods, while the transfer-matrix renormalization-group method is invoked to study the thermodynamics. It is found that the magnon spectra consist of a gapless and two gapped branches. Two branches in case (C) have intersections. The coupling dependence of low-energy gaps are analyzed. In a magnetic field, a $m=\frac{3}{2}$ ( $m$ is the magnetization per unit cell) plateau is observed for case (A), while two plateaux at $m=\frac{1}{2}$ and $\frac{3}{2}$ are observed for cases (B) and (C). Between the two plateaux in cases (B) and (C), the sublattice magnetizations for the spins coupled by ferromagnetic interactions have decreasing regions with increasing the magnetic field. At finite temperature, the zero-field susceptibility temperature product $\ensuremath{\chi}T$ and specific heat exhibit distinct exotic features with varying the couplings and temperature for different cases. $\ensuremath{\chi}T$ is found to converge as $T\ensuremath{\rightarrow}0$, which is different from the divergent behavior in the spin- $(\frac{1}{2},1)$ mixed-spin chain without pendants. The observed thermodynamic behaviors are also discussed with the help of their low-lying excitations.The magnetic and thermodynamic properties of a ferrimagnetic decorated spin-$(\frac{1}{2},1)$ Heisenberg chain with spin-1 pendant spins are investigated for three cases: (A) ${J}_{1},{J}_{2}>0$; (B) ${J}_{1}>0$ and ${J}_{2}<0$; and (C) ${J}_{1}<0$ and ${J}_{2}>0$, where ${J}_{1}$ and ${J}_{2}$ are the exchange couplings between spins in the chain and along the rung, respectively. The low-lying and magnetic properties are explored jointly by the real-space renormalization group, spin wave, and density-matrix renormalization-group methods, while the transfer-matrix renormalization-group method is invoked to study the thermodynamics. It is found that the magnon spectra consist of a gapless and two gapped branches. Two branches in case (C) have intersections. The coupling dependence of low-energy gaps are analyzed. In a magnetic field, a $m=\frac{3}{2}$ ($m$ is the magnetization per unit cell) plateau is observed for case (A), while two plateaux at $m=\frac{1}{2}$ and $\frac{3}{2}$ are observed for cases (B) and (C). Between the two plateaux in cases (B) and (C), the sublattice magnetizations for the spins coupled by ferromagnetic interactions have decreasing regions with increasing the magnetic field. At finite temperature, the zero-field susceptibility temperature product $\ensuremath{\chi}T$ and specific heat exhibit distinct exotic features with varying the couplings and temperature for different cases. $\ensuremath{\chi}T$ is found to converge as $T\ensuremath{\rightarrow}0$, which is different from the divergent behavior in the spin-$(\frac{1}{2},1)$ mixed-spin chain without pendants. The observed thermodynamic behaviors are also discussed with the help of their low-lying excitations.

arXiv:1006.0794Physical Review BJun 21, 201022 citations

Low temperature thermodynamics of quantum spin chains

Naobumi Honda, Harukazu Igarashi

Physics Letters AFeb 1, 19822 citations

Dual thermal pseudocritical features in a spin-1/2 Ising chain with twin-diamond geometry

Onofre Rojas

We study the coupled twin-diamond chain, a decorated one-dimensional Ising model motivated by the magnetic structure of Cu_{2}(TeO_{3})_{2}Br_{2}. By applying an exact mapping to an effective Ising chain, we obtain the full thermodynamic description of the system through a compact transfer-matrix formulation. The ground-state analysis reveals five distinct phases, including two frustrated sectors with extensive degeneracy. These frustrated regions give rise to characteristic entropy plateaus and separate the ordered phases in the zero-temperature diagram. At low temperatures the model exhibits peculiar sharp yet continuous variations of entropy, magnetization, and response functions, reflecting clear signatures of pseudotransition behavior. The coupled twin-diamond chain thus provides an exactly solvable setting in which competing local configurations and internal frustration lead to pronounced dual pseudocritical features in one dimension.We study the coupled twin-diamond chain, a decorated one-dimensional Ising model motivated by the magnetic structure of Cu_{2}(TeO_{3})_{2}Br_{2}. By applying an exact mapping to an effective Ising chain, we obtain the full thermodynamic description of the system through a compact transfer-matrix formulation. The ground-state analysis reveals five distinct phases, including two frustrated sectors with extensive degeneracy. These frustrated regions give rise to characteristic entropy plateaus and separate the ordered phases in the zero-temperature diagram. At low temperatures the model exhibits peculiar sharp yet continuous variations of entropy, magnetization, and response functions, reflecting clear signatures of pseudotransition behavior. The coupled twin-diamond chain thus provides an exactly solvable setting in which competing local configurations and internal frustration lead to pronounced dual pseudocritical features in one dimension.

arXiv:2511.18596Physical review. EFeb 2, 20265 citations

Thermodynamics of quantum spin chains

Alessandro Cuccoli, V. Tognetti, Ruggero Vaia +1 more

Springer eBooksApr 7, 20080 citations

Exactly Solvable Decorated-Kekulé-lattice Kitaev Model

Tomonari Mizoguchi

We propose the decorated-Kekulé-lattice Kitaev model, which is exactly solvable at any temperature. Similar to the decorated honeycomb model proposed in our previous work [J. Phys. Soc. Jpn. 91, 124709 (2022)], the exact solvability arises from the fact that the spins on the decorated sites become conserved quantities (i.e., classical variables) and serve as an effective field acting on the remaining spins. For a given sector of the classical variables, the remaining spins are described by the Hamiltonian of ensemble of decoupled two-site transverse Ising models, with eigenenergies being independent of the configuration of the classical variables. This enables us to calculate the partition function exactly, and hence the thermodynamic quantities are obtained at any temperature. Our result indicates that the site decoration for the compass-type models is a ubiquitous method to obtain the models that are exactly solvable at finite temperature.We propose the decorated-Kekulé-lattice Kitaev model, which is exactly solvable at any temperature. Similar to the decorated honeycomb model proposed in our previous work [J. Phys. Soc. Jpn. 91, 124709 (2022)], the exact solvability arises from the fact that the spins on the decorated sites become conserved quantities (i.e., classical variables) and serve as an effective field acting on the remaining spins. For a given sector of the classical variables, the remaining spins are described by the Hamiltonian of ensemble of decoupled two-site transverse Ising models, with eigenenergies being independent of the configuration of the classical variables. This enables us to calculate the partition function exactly, and hence the thermodynamic quantities are obtained at any temperature. Our result indicates that the site decoration for the compass-type models is a ubiquitous method to obtain the models that are exactly solvable at finite temperature.

Journal of the Physical Society of JapanJan 23, 20260 citations

The magnetic and thermodynamic properties of a ferrimagnetic decorated spin-

(\frac{1}{2},1)

Heisenberg chain with spin-1 pendant spins are investigated for three cases: (A)

{J}_{1},{J}_{2}>0

; (B)

{J}_{1}>0

and

{J}_{2}<0

; and (C)

{J}_{1}<0

and

{J}_{2}>0

, where

{J}_{1}

and

{J}_{2}

are the exchange couplings between spins in the chain and along the rung, respectively. The low-lying and magnetic properties are explored jointly by the real-space renormalization group, spin wave, and density-matrix renormalization-group methods, while the transfer-matrix renormalization-group method is invoked to study the thermodynamics. It is found that the magnon spectra consist of a gapless and two gapped branches. Two branches in case (C) have intersections. The coupling dependence of low-energy gaps are analyzed. In a magnetic field, a

m=\frac{3}{2}

(

m

is the magnetization per unit cell) plateau is observed for case (A), while two plateaux at

m=\frac{1}{2}

and

\frac{3}{2}

are observed for cases (B) and (C). Between the two plateaux in cases (B) and (C), the sublattice magnetizations for the spins coupled by ferromagnetic interactions have decreasing regions with increasing the magnetic field. At finite temperature, the zero-field susceptibility temperature product $\ensuremath{\chi}T$ and specific heat exhibit distinct exotic features with varying the couplings and temperature for different cases. $\ensuremath{\chi}T$ is found to converge as $T\ensuremath{\rightarrow}0$, which is different from the divergent behavior in the spin-

(\frac{1}{2},1)

mixed-spin chain without pendants. The observed thermodynamic behaviors are also discussed with the help of their low-lying excitations.