The "star-triangle" and "decoration" transformations are generalized so as to apply to arbitrary mechanical systems coupled to the spins of a standard Ising net. This leads to exact solutions for further plane Ising nets and also for lattices in which the spins on alternate sites have a magnitude greater than $S=\frac{1}{2}$ . A general class of antiferromagnetic Ising models is constructed; exact closed expressions can be derived for all the thermodynamic and magnetic properties of these models in an arbitrary magnetic field.The magnetizations and susceptibilities of Ising nets in which different spins have different magnetic moments are investigated and a valuable relation between the susceptibilities of the honeycomb and triangular lattices is derived. It is shown how correlation functions involving a given spin can be expressed in terms of correlations involving the nearest-neighbor spins instead.The "star-triangle" and "decoration" transformations are generalized so as to apply to arbitrary mechanical systems coupled to the spins of a standard Ising net. This leads to exact solutions for further plane Ising nets and also for lattices in which the spins on alternate sites have a magnitude greater than $S=\frac{1}{2}$. A general class of antiferromagnetic Ising models is constructed; exact closed expressions can be derived for all the thermodynamic and magnetic properties of these models in an arbitrary magnetic field.The magnetizations and susceptibilities of Ising nets in which different spins have different magnetic moments are investigated and a valuable relation between the susceptibilities of the honeycomb and triangular lattices is derived. It is shown how correlation functions involving a given spin can be expressed in terms of correlations involving the nearest-neighbor spins instead.

Physical ReviewFeb 15, 1959401 citations

Emergence of quantum spin frustration in spin-1/2 Ising-Heisenberg model on a decorated honeycomb lattice

Onofre Rojas

We study the spin-1/2 Ising-XXZ model on a decorated honeycomb lattice composed of five spins per unit cell, one Ising spin, and four Heisenberg spins. This model involving the Heisenberg exchange interaction is one of the few models that can be exactly solvable through the generalized star-triangle transformation. The significance of this model is its close relationship to the fully decorated quantum Heisenberg honeycomb lattice since 4/5 of the particles are Heisenberg spins. We investigate the phase diagram at zero temperature and identify a relevant quantum spin frustrated phase resulting from the contribution of quantum Heisenberg exchange interaction. We obtain an exact residual entropy for the quantum spin frustrated phase, which coincides with the residual entropy of the antiferromagnetic spin-1/2 Ising model on a triangular lattice. We also thoroughly explore its thermodynamic properties, focusing mainly on the frustrated region such as entropy, specific heat, spontaneous magnetization, and critical temperature under several conditions.We study the spin-1/2 Ising-XXZ model on a decorated honeycomb lattice composed of five spins per unit cell, one Ising spin, and four Heisenberg spins. This model involving the Heisenberg exchange interaction is one of the few models that can be exactly solvable through the generalized star-triangle transformation. The significance of this model is its close relationship to the fully decorated quantum Heisenberg honeycomb lattice since 4/5 of the particles are Heisenberg spins. We investigate the phase diagram at zero temperature and identify a relevant quantum spin frustrated phase resulting from the contribution of quantum Heisenberg exchange interaction. We obtain an exact residual entropy for the quantum spin frustrated phase, which coincides with the residual entropy of the antiferromagnetic spin-1/2 Ising model on a triangular lattice. We also thoroughly explore its thermodynamic properties, focusing mainly on the frustrated region such as entropy, specific heat, spontaneous magnetization, and critical temperature under several conditions.

arXiv:2206.06104Physical review. EJul 11, 20221 citation

Phase transitions in the Ising model

Valeriy A Ryabov

Institute of Physics eBooksAug 1, 20180 citations

Thermodynamics of the spin- 12 Heisenberg antiferromagnet on the star lattice

Adrien Reingruber, Nils Caci, Stefan Weßel +1 more

Using a combination of quantum Monte Carlo simulations in adapted cluster bases, the finite-temperature Lanczos method, and an effective Hamiltonian approach, we explore the thermodynamic properties of the spin-1/2 Heisenberg antiferromagnet on the star lattice. We consider various parameter regimes on this strongly frustrated Archimedean lattice, including the case of homogeneous couplings as well as the distinct parameter regimes of dominant vs weak dimer coupling. For the latter case, we explore the quantum phase diagram in the presence of inhomogeneous trimer couplings, preserving inversion symmetry. We compare the efficiency of different cluster decoupling schemes for the quantum Monte Carlo simulations in terms of the sign problem, contrast the thermodynamic properties to those of other strongly frustrated quantum magnets such as the kagome lattice model, and comment on previous results from tensor-network calculations regarding a valence bond crystal phase in the regime of weak dimer coupling. Finally, we relate our results to recently reported experimental findings on a Cu-based quantum magnetic spin-1/2 compound with an underlying star lattice structure.Using a combination of quantum Monte Carlo simulations in adapted cluster bases, the finite-temperature Lanczos method, and an effective Hamiltonian approach, we explore the thermodynamic properties of the spin-1/2 Heisenberg antiferromagnet on the star lattice. We consider various parameter regimes on this strongly frustrated Archimedean lattice, including the case of homogeneous couplings as well as the distinct parameter regimes of dominant vs weak dimer coupling. For the latter case, we explore the quantum phase diagram in the presence of inhomogeneous trimer couplings, preserving inversion symmetry. We compare the efficiency of different cluster decoupling schemes for the quantum Monte Carlo simulations in terms of the sign problem, contrast the thermodynamic properties to those of other strongly frustrated quantum magnets such as the kagome lattice model, and comment on previous results from tensor-network calculations regarding a valence bond crystal phase in the regime of weak dimer coupling. Finally, we relate our results to recently reported experimental findings on a Cu-based quantum magnetic spin-1/2 compound with an underlying star lattice structure.

arXiv:2311.13393Physical review. B./Physical review. BMar 11, 20245 citations

S=\frac{1}{2}

. A general class of antiferromagnetic Ising models is constructed; exact closed expressions can be derived for all the thermodynamic and magnetic properties of these models in an arbitrary magnetic field.The magnetizations and susceptibilities of Ising nets in which different spins have different magnetic moments are investigated and a valuable relation between the susceptibilities of the honeycomb and triangular lattices is derived. It is shown how correlation functions involving a given spin can be expressed in terms of correlations involving the nearest-neighbor spins instead.