Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

arXiv:cond-mat/0701071 · Physical Review B

Exact solution of the mixed-spin Ising model on a decorated square lattice with two different kinds of decorating spins on horizontal and vertical bonds

Jozef Strečka, Lucia Čanová, M. Jaščur

Published Jul 11, 2007• 22 citations
arXivHTMLPDF

Abstract

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.

DOI
10.1103/physrevb.76.014413

Related papers

Spontaneous Magnetization and Phase Diagrams of the Mixed Spin-1/2 and Spin-S Ising Model on the Bethe Lattice

Jozef Strečka, Cesur Ekiz

The effect of uniaxial single-ion anisotropy on magnetic and critical properties of the mixed spin-1/2 and spin-S (S > 1/2) Ising model on a three-coordinated Bethe lattice is rigorously examined with the help of star-triangle transformation and exact recursion relations.In particular, our attention is focused on the ferrimagnetic version of the model, which exhibits diverse temperature dependences of the total and both sublattice magnetizations.It is shown that the critical behavior of the mixed-spin Ising model on the Bethe lattice basically depends on whether the quantum spin number S is integer or half-odd-integer.

Acta Physica Polonica A•Apr 1, 2017•6 citations

Strong- and Weak-Universal Critical Behaviour of a Mixed-Spin Ising Model with Triplet Interactions on the Union Jack (Centered Square) Lattice

Jozef Strečka

The mixed spin-1/2 and spin-S Ising model on the Union Jack (centered square) lattice with four different three-spin (triplet) interactions and the uniaxial single-ion anisotropy is exactly solved by establishing a rigorous mapping equivalence with the corresponding zero-field (symmetric) eight-vertex model on a dual square lattice. A rigorous proof of the aforementioned exact mapping equivalence is provided by two independent approaches exploiting either a graph-theoretical or spin representation of the zero-field eight-vertex model. An influence of the interaction anisotropy as well as the uniaxial single-ion anisotropy on phase transitions and critical phenomena is examined in particular. It is shown that the considered model exhibits a strong-universal critical behaviour with constant critical exponents when considering the isotropic model with four equal triplet interactions or the anisotropic model with one triplet interaction differing from the other three. The anisotropic models with two different triplet interactions, which are pairwise equal to each other, contrarily exhibit a weak-universal critical behaviour with critical exponents continuously varying with a relative strength of the triplet interactions as well as the uniaxial single-ion anisotropy. It is evidenced that the variations of critical exponents of the mixed-spin Ising models with the integer-valued spins S differ basically from their counterparts with the half-odd-integer spins S.

arXiv:1801.02676•Entropy•Jan 29, 2018•4 citations

Thermal phase transitions in a mixed-spin Ising model on the Lieb lattice: Exact results beyond zero magnetic field

Jozef Strečka, Katarína Karľová

We investigate the ground-state and finite-temperature properties of a mixed spin-1/2 and spin-1 Ising model on a decorated square (Lieb) lattice incorporating a uniaxial single-ion anisotropy and magnetic field. By employing the generalized decoration-iteration transformation, the model is mapped exactly onto an effective spin-1/2 Ising model on the square lattice characterized by an effective nearest-neighbor interaction and an effective field. The studied model consequently becomes exactly solvable even for finite values of the applied magnetic field whenever the effective field vanishes. The ground-state analysis reveals three distinct phases: ferrimagnetic phase (FRI), disordered phase (DP), and ferromagnetic (FM) phase. The ground-state boundary between FRI and DP phases gives rise to a dome-shaped surface of discontinuous thermal phase transitions, which is terminated by a line of Ising-type critical points associated with continuous thermal phase transitions. Both continuous and discontinuous thermal phase transitions belong to the exactly solvable parameter regime defined by a vanishing effective field in spite of the fact that the applied magnetic field is finite. Two consecutive discontinuous thermally-induced reentrant phase transitions DP-FRI-DP are identified in a narrow parameter region. The exact analytical predictions including reentrance, field- and thermally-driven phase transitions are independently verified by classical Monte Carlo simulations.

arXiv:2607.11661•Jul 13, 2026•0 citations

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

Jozef Strečka, A Tanaka, M Jaščur

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.

arXiv:0908.2880•Journal of Physics Conference Series•Jan 1, 2010•9 citations

Exact phase diagram for the mixed spin-1/2 and spin-S Ising models on the square lattice

A. Dakhama, Mouhcine Azhari, Noureddine Benayad

We propose a new approach which permits us to obtain exact results for the mixed spin-1/2 and Spin- S ( S > 1/2) Ising models with single ion anisotropy Δ on the square lattice. We drive an explicit expression for the critical temperature for arbitrary values of S. We determine the exact phase diagrams for different values of S , and we show that there is no tricritical point. For S integer, there is no long range order when the anisotropy exceeds a critical value which is independent of S . Furthermore, the exact Ising transition temperature T C is always recovered, for any values of S, in the limit of Δ → − ∞ . These exact results are based on a conjecture which extend the analyticity of the n-spin-1/2 correlations functions (except at T = T C (Ising)) for any finite number n, to n → ∞ . This is confirmed by our calculations since our results are practically similar to those obtained by Monte Carlo simulations for S = 1, 2 and 3/2.

Journal of Physics Communications•Jun 11, 2018•15 citations

Monte Carlo studies of critical phenomena in mixed spin-3/2 and spin-5/2 Ising model on square lattice

N. De La Espriella, J. Madera Yancez, M. S. Páez Mesa

"We used a Monte Carlo simulation to analize the magnetic behavior of Ising model of mixed spins S A i = ß3=2 ; ß1=2 and æ B j = ß 5 = 2 ; ß 3 = 2 ; ß 1 = 2 , on a square lattice. Were studied the possible critical phenomena that may emerge in the region around the multiphase point (D= j J 1 j = ° 3 ;J 2 = j J 1 j = 1) and the dependence of the phase diagrams with the intensities of the anisotropy field of single ion (D= j J 1 j ) and the ferromagnetic coupling of exchange spin S A i (J 2 = j J 1 j). The system displays first order phase transitions in a certain range of the parameters of the Hamiltonian, which depend on D= j J 1 j and j J 2 = j J 1 j . In the plane (D= j J 1 j ;k B T= j J 1 j), the de- crease of j D= j J 1 jj , implies that the critical temperature, T c , increases and the first order transition temperature, T t , decreases. In the plane (J2 = j J 1 j ;k B T= j J 1 j ), T c increases with the increasing of J 2 = j J 1 j , while that T t decreases."

Revista Mexicana de Física•Jan 1, 2014•7 citations
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​ (SB\ensuremath≠SC)({S}_{\mathrm{B}}\ensuremath{\ne}{S}_{\mathrm{C}})(SB​\ensuremath=SC​) 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.
The effect of uniaxial single-ion anisotropy on magnetic and critical properties of the mixed spin-1/2 and spin-S (S > 1/2) Ising model on a three-coordinated Bethe lattice is rigorously examined with the help of star-triangle transformation and exact recursion relations.In particular, our attention is focused on the ferrimagnetic version of the model, which exhibits diverse temperature dependences of the total and both sublattice magnetizations.It is shown that the critical behavior of the mixed-spin Ising model on the Bethe lattice basically depends on whether the quantum spin number S is integer or half-odd-integer.
The mixed spin-1/2 and spin-S Ising model on the Union Jack (centered square) lattice with four different three-spin (triplet) interactions and the uniaxial single-ion anisotropy is exactly solved by establishing a rigorous mapping equivalence with the corresponding zero-field (symmetric) eight-vertex model on a dual square lattice. A rigorous proof of the aforementioned exact mapping equivalence is provided by two independent approaches exploiting either a graph-theoretical or spin representation of the zero-field eight-vertex model. An influence of the interaction anisotropy as well as the uniaxial single-ion anisotropy on phase transitions and critical phenomena is examined in particular. It is shown that the considered model exhibits a strong-universal critical behaviour with constant critical exponents when considering the isotropic model with four equal triplet interactions or the anisotropic model with one triplet interaction differing from the other three. The anisotropic models with two different triplet interactions, which are pairwise equal to each other, contrarily exhibit a weak-universal critical behaviour with critical exponents continuously varying with a relative strength of the triplet interactions as well as the uniaxial single-ion anisotropy. It is evidenced that the variations of critical exponents of the mixed-spin Ising models with the integer-valued spins S differ basically from their counterparts with the half-odd-integer spins S.
We investigate the ground-state and finite-temperature properties of a mixed spin-1/2 and spin-1 Ising model on a decorated square (Lieb) lattice incorporating a uniaxial single-ion anisotropy and magnetic field. By employing the generalized decoration-iteration transformation, the model is mapped exactly onto an effective spin-1/2 Ising model on the square lattice characterized by an effective nearest-neighbor interaction and an effective field. The studied model consequently becomes exactly solvable even for finite values of the applied magnetic field whenever the effective field vanishes. The ground-state analysis reveals three distinct phases: ferrimagnetic phase (FRI), disordered phase (DP), and ferromagnetic (FM) phase. The ground-state boundary between FRI and DP phases gives rise to a dome-shaped surface of discontinuous thermal phase transitions, which is terminated by a line of Ising-type critical points associated with continuous thermal phase transitions. Both continuous and discontinuous thermal phase transitions belong to the exactly solvable parameter regime defined by a vanishing effective field in spite of the fact that the applied magnetic field is finite. Two consecutive discontinuous thermally-induced reentrant phase transitions DP-FRI-DP are identified in a narrow parameter region. The exact analytical predictions including reentrance, field- and thermally-driven phase transitions are independently verified by classical Monte Carlo simulations.
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.
We propose a new approach which permits us to obtain exact results for the mixed spin-1/2 and Spin- S ( S > 1/2) Ising models with single ion anisotropy Δ on the square lattice. We drive an explicit expression for the critical temperature for arbitrary values of S. We determine the exact phase diagrams for different values of S , and we show that there is no tricritical point. For S integer, there is no long range order when the anisotropy exceeds a critical value which is independent of S . Furthermore, the exact Ising transition temperature T C is always recovered, for any values of S, in the limit of Δ → − ∞ . These exact results are based on a conjecture which extend the analyticity of the n-spin-1/2 correlations functions (except at T = T C (Ising)) for any finite number n, to n → ∞ . This is confirmed by our calculations since our results are practically similar to those obtained by Monte Carlo simulations for S = 1, 2 and 3/2.
"We used a Monte Carlo simulation to analize the magnetic behavior of Ising model of mixed spins S A i = ß3=2 ; ß1=2 and æ B j = ß 5 = 2 ; ß 3 = 2 ; ß 1 = 2 , on a square lattice. Were studied the possible critical phenomena that may emerge in the region around the multiphase point (D= j J 1 j = ° 3 ;J 2 = j J 1 j = 1) and the dependence of the phase diagrams with the intensities of the anisotropy field of single ion (D= j J 1 j ) and the ferromagnetic coupling of exchange spin S A i (J 2 = j J 1 j). The system displays first order phase transitions in a certain range of the parameters of the Hamiltonian, which depend on D= j J 1 j and j J 2 = j J 1 j . In the plane (D= j J 1 j ;k B T= j J 1 j), the de- crease of j D= j J 1 jj , implies that the critical temperature, T c , increases and the first order transition temperature, T t , decreases. In the plane (J2 = j J 1 j ;k B T= j J 1 j ), T c increases with the increasing of J 2 = j J 1 j , while that T t decreases."