A spin-one Ising model on the Bethe lattice

Chakraborty, K.G.; Morita, Tohru

doi:10.1016/0378-4371(85)90177-3

Cited by 29 publications

(13 citation statements)

References 19 publications

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“…A spin-1 Ising model, which was initially introduced by Blume-Emery-Griffiths (BEG) [31] in connection with phase separation and superfluid ordering in He 3 -He 4 mixtures. The BEG model has played an important role in the development of the theory of multicritical phenomena associated with various physical systems [33] and has extensively been investigated in the literature [6,7].…”

Section: A Most General Spin-s Modelmentioning

confidence: 99%

“…The BEG model on the Bethe lattice was studied in Refs. [6,7]. The model has played an important role in the development of the theory of tricritical phenomena [33].…”

Section: Spin -1 Ising Modelmentioning

confidence: 99%

“…The Bethe [1] and the Bethe-like [2] lattices have been widely used in solid state and statistical physics [3][4][5][6][7][8][9][10][11][12][13][14][15][16][17][18] as they represent underlying lattices for which many problems can be solved exactly. The Bethe lattice has attracted particular interest because it usually reflects essential features of systems, even when conventional mean -field theories fail [11].…”

Section: Introductionmentioning

confidence: 99%

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Exact correlation functions of Bethe lattice spin models in external magnetic fields

Измаилян

1998

Phys. Rev. E

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We develop a transfer matrix method to compute exactly the spin-spin correlation functions < s 0 s n > of Bethe lattice spin models in the external magnetic field h and for any temperature T . We first compute < s 0 s n > for the most general spin -S Ising model, which contains all possible single-ion and nearest-neighbor pair interactions. This general spin -S Ising model includes the spin-1/2 simple Ising model and the Blume-Emery-Griffiths (BEG) model as special cases. From the spin-spin correlation functions, we obtain functions of correlation length, ξ(T, h), for the simple Ising model and BEG model, which show interesting scaling and divergent behavior as h → 0 and T approaches the critical temperature T c . Our method to compute exact spinspin correlation functions may be applied to other Ising-type models on Bethe and Bethe-like lattices.

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Section: A Most General Spin-s Modelmentioning

confidence: 99%

“…The BEG model on the Bethe lattice was studied in Refs. [6,7]. The model has played an important role in the development of the theory of tricritical phenomena [33].…”

Section: Spin -1 Ising Modelmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Exact correlation functions of Bethe lattice spin models in external magnetic fields

Измаилян

1998

Phys. Rev. E

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“…Our aim is to evaluate the partition function for the BEG model on a Bethe lattice and, in particular, to determine the tri-critical point which will allow us to find the critical number of invisible states required to effect a first-order transition. This may be done in a standard manner for the Bethe lattice by evaluating the partition function recursively, shell by shell, starting at the central vertex given by i = 0 [12,13,15,16]. The partition function can be written as…”

Section: The Beg Model On a Bethe Lattice And Its Tri-critical Pointmentioning

confidence: 99%

Potts models with invisible states on general Bethe lattices

Ananikian¹,

Izmailyan²,

Johnston³

et al. 2013

J. Phys. A: Math. Theor.

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Abstract.The number of so-called invisible states which need to be added to the q-state Potts model to transmute its phase transition from continuous to first order has attracted recent attention. In the q = 2 case, a Bragg-Williams, mean-field approach necessitates four such invisible states while a 3-regular, random-graph formalism requires seventeen. In both of these cases, the changeover from second-to first-order behaviour induced by the invisible states is identified through the tricritical point of an equivalent BlumeEmery-Griffiths model.Here we investigate the generalised Potts model on a Bethe lattice with z neighbours. We show that, in the q = 2 case, r c (z) = 4z 3(z − 1)states are required to manifest the equivalent Blume-Emery-Griffiths tricriticality. When z = 3, the 3-regular, random-graph result is recovered, while z → ∞ delivers the Bragg-Williams, mean-field result.arXiv:1307.2803v1 [cond-mat.stat-mech]

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“…It has subsequently been studied by the well known methods in equilibrium statistical physics such as, the mean-field approximation [3], the generalized constant coupling approximation [4], the effective field theory [5], the cluster variation methods [6] and the finite cluster approximation [7]. The exact solution of the model on the Bethe lattice was also studied [8].…”

Section: Introductionmentioning

confidence: 99%

Dynamic Dipole and Quadrupole Phase Transitions in the Kinetic Spin-1 Model

Keskín

Canko

Kantar

2006

Int. J. Mod. Phys. C

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The dynamic phase transitions have been studied, within a mean-field approach, in the kinetic spin-1 Ising model Hamiltonian with arbitrary bilinear and biquadratic pair interactions in the presence of a time varying (sinusoidal) magnetic field by using the Glauber-type stochastic dynamics. The nature (first-or second-order) of the transition is characterized by investigating the behavior of the thermal variation of the dynamic order parameters. The dynamic phase transitions (DPTs) are obtained and the phase diagrams are constructed in the temperature and magnetic field amplitude plane and found six fundamental types of phase diagrams. Phase diagrams exhibit one or two dynamic tricritical points depending on the biquadratic interaction (K). Besides the disordered (D) and ferromagnetic (F) phases, the FQ + D, F + FQ and F + D coexistence phase regions also exist in the system and the F and F + D phases disappear for high values of K.

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A spin-one Ising model on the Bethe lattice

Cited by 29 publications

References 19 publications

Exact correlation functions of Bethe lattice spin models in external magnetic fields

Exact correlation functions of Bethe lattice spin models in external magnetic fields

Potts models with invisible states on general Bethe lattices

Dynamic Dipole and Quadrupole Phase Transitions in the Kinetic Spin-1 Model

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