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

International Journal of Modern Physics B

RANDOM MIXED SPINS ISING MODEL ON THE HONEYCOMB LATTICE

J. R. Gonçalves, L.L. Gonçalves

Published Jul 10, 1994• 1 citation
Publisher

Abstract

The Ising model on the honeycomb lattice with spins of magnitudes 1/2 and s with random exchange constant and random uniaxial anisotropy is considered. The two cases are studied separately, and in both cases binary annealed distributions of the random parameters are considered. An exact solution is obtained by mapping the model onto the uniform spin 1/2 Ising model on the triangular lattice, and the transition temperature is determined as a function of the parameters for arbitrary s. Explicit results are presented for s=1 and s=3/2, and it is shown that some critical parameters, surprisingly, are not universal.

DOI
10.1142/s0217979294000816

Related papers

Uniaxial Anisotropy Effects in the Ising Model: an Exactly Soluble Model

L.L. Gonçalves

The effect of the uniaxial anisotropy in an Ising model consisting of mixed spins of magnitudes s and 1/2, on the honeycomb lattice, is studied. The exact solution is determined by mapping the model onto an effective spin 1/2 Ising model on the triangular lattice. The transition temperature is obtained as a function of the parameters and it is shown that for s integer there is no long range order for the parameter values in a determined region which is independent of the value of s. The critical exponents are obtained and it is shown that they are the same as those of the two-dimensional spin 1/2 Ising model.

Physica Scripta•Sep 1, 1985•106 citations

Uniaxial Anisotropy and Next-Nearest-Neighbour Interaction Effects in the 2D Ising Model

L.L. Gonçalves

An Ising model consisting of mixed spins of magnitudes s and 1/2, on the honeycomb lattice is considered. The spins of a given magnitude occupy one of the two equivalent sublattices of the honeycomb lattice and the next-nearest-neighbour interactions are allowed between the spins 1/2 only. The exact solution of the problem, in the presence of uniaxial anisotropy, is obtained by mapping the model onto an effective spin 1/2 Ising model on a triangular lattice. The transition temperature as a function of the parameters of the Hamiltonian is explicitly determined when the second neighbour interaction is allowed in one direction or two directions of the sublattice occupied by the spins 1/2. It is shown that in the first case, frustration effects are the dominant mechanism for suppression of the ground state long range order, irrespective of s being integer or half integer. The important feature in the second case is the appearance of three transition temperatures for some values of the parameters, and this will imply in a reentrant critical surface. Explicit results are worked out for s = 1 and s = 3/2, which present the main features of the model. By using a general result for decorated lattices the critical exponents are determined for arbitrary s .

Physica Scripta•Feb 1, 1987•2 citations

The dilute spin-one Ising model on a honeycomb lattice

Viktor Urumov

Given some restriction on the interaction parameters, the critical temperature for the spin-one Ising model on a honeycomb lattice described with the Blume-Emery-Griffiths Hamiltonian with random non-magnetic impurities in equilibrium (annealed site-disorder case) is obtained exactly.

Journal of Physics Condensed Matter•Feb 13, 1989•7 citations

MONTE CARLO STUDY OF THE PHASE DIAGRAM OF ISING FERROMAGNET WITH MIXED SPINS OF S=l/2 AND S=l WITH A CRYSTAL FIELD INTERACTION ON THE HONEYCOMB LATTICE

ZHANG GUO-MING, YANG CHUAN-ZHANG, 苏州大学物理系,苏州215006

The single-spin-flip Metropolis-Monte-Carlo algorithm is applied to the study of phase diagram of Ising ferromagnet with mixed spins of S = l/2 and S = 1 with a crystal field interaction on the honeycomb lattice. The phase diagram we obtained is very close to the exact solutions and better than the results of effective field theory with correlations. All these make us arrixe the conclusion that the Metropolis Monte Carlo algorithm can also be used to study the mixed-spin model.

Acta Physica Sinica•Jan 1, 1993•1 citation

CRITICAL BEHAVIOR OF THE QUENCHED RANDOM MIXED-SPIN ISING MODEL

Maurício Godoy, W. Figueiredo

In this work, we simulated a quenched random mixed-spin Ising model on the square lattice. The model system consists of two different particles with spins σ = 1/2 (states ±1/2) and S = 1 (states ±1, 0). These particles are randomly distributed on the lattice, and we considered only nearest-neighbor interactions. This model can represent a random magnetic binary alloy AxB1-x, obtained from the high-temperature quenching of a liquid mixture. We performed Monte Carlo simulations for several lattice sizes and temperatures, and we found its critical temperature through the reduced fourth-order cumulant. We also determined the magnetization, the susceptibility, and the specific heat as a function of temperature. We used finite-size scaling arguments to estimate the critical exponents β, γ, and ν of the model. We showed that the quenched model is in the same universality class of the two-dimensional pure Ising model. We also investigated the sample to sample fluctuations that occur in the values of the thermodynamic quantities in order to describe the self-averaging properties at the critical point.

International Journal of Modern Physics C•Jan 1, 2009•9 citations

Exact Solution for a Spin-1 Model on Honeycomb/Triangular Lattices

TANG KUN-FA, HU JIA-ZHEN

A generalized Blume-Emery-Criffiths model on the honeycomb lattice is solved exactly in a parameter subspace. Ising transition critical surfaces are found for this model with a zero and a pure imaginary field respectively. And the mapping onto a triangular spin-1 model is made.

Communications in Theoretical Physics•Jan 1, 1989•0 citations
The Ising model on the honeycomb lattice with spins of magnitudes 1/2 and s with random exchange constant and random uniaxial anisotropy is considered. The two cases are studied separately, and in both cases binary annealed distributions of the random parameters are considered. An exact solution is obtained by mapping the model onto the uniform spin 1/2 Ising model on the triangular lattice, and the transition temperature is determined as a function of the parameters for arbitrary s. Explicit results are presented for s=1 and s=3/2, and it is shown that some critical parameters, surprisingly, are not universal.
The effect of the uniaxial anisotropy in an Ising model consisting of mixed spins of magnitudes s and 1/2, on the honeycomb lattice, is studied. The exact solution is determined by mapping the model onto an effective spin 1/2 Ising model on the triangular lattice. The transition temperature is obtained as a function of the parameters and it is shown that for s integer there is no long range order for the parameter values in a determined region which is independent of the value of s. The critical exponents are obtained and it is shown that they are the same as those of the two-dimensional spin 1/2 Ising model.
An Ising model consisting of mixed spins of magnitudes s and 1/2, on the honeycomb lattice is considered. The spins of a given magnitude occupy one of the two equivalent sublattices of the honeycomb lattice and the next-nearest-neighbour interactions are allowed between the spins 1/2 only. The exact solution of the problem, in the presence of uniaxial anisotropy, is obtained by mapping the model onto an effective spin 1/2 Ising model on a triangular lattice. The transition temperature as a function of the parameters of the Hamiltonian is explicitly determined when the second neighbour interaction is allowed in one direction or two directions of the sublattice occupied by the spins 1/2. It is shown that in the first case, frustration effects are the dominant mechanism for suppression of the ground state long range order, irrespective of s being integer or half integer. The important feature in the second case is the appearance of three transition temperatures for some values of the parameters, and this will imply in a reentrant critical surface. Explicit results are worked out for s = 1 and s = 3/2, which present the main features of the model. By using a general result for decorated lattices the critical exponents are determined for arbitrary s .
In this work, we simulated a quenched random mixed-spin Ising model on the square lattice. The model system consists of two different particles with spins σ = 1/2 (states ±1/2) and S = 1 (states ±1, 0). These particles are randomly distributed on the lattice, and we considered only nearest-neighbor interactions. This model can represent a random magnetic binary alloy AxB1-x, obtained from the high-temperature quenching of a liquid mixture. We performed Monte Carlo simulations for several lattice sizes and temperatures, and we found its critical temperature through the reduced fourth-order cumulant. We also determined the magnetization, the susceptibility, and the specific heat as a function of temperature. We used finite-size scaling arguments to estimate the critical exponents β, γ, and ν of the model. We showed that the quenched model is in the same universality class of the two-dimensional pure Ising model. We also investigated the sample to sample fluctuations that occur in the values of the thermodynamic quantities in order to describe the self-averaging properties at the critical point.