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Blume, M.; Emery, V. J.; Griffiths, Robert B.

doi:10.1103/physreva.4.1071

Cited by 1,534 publications

(837 citation statements)

References 13 publications

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“…The bulk phase diagram of 3 He-4 He is well described by the BlumeEmery-Griffiths (BEG) model [6] which is a spin-1 system with nearest neighbor interactions and a uniform anisotropy external field distinguishing only between the ±1 and 0 values of the spin. Its generalization to the 3 He-4 He mixture in a porous medium is described by the hamiltonian [1] Since we are going to study a model for 3 He- 4 He mixtures in aerogel, we will let each ∆ i take the value ∆ 0 or ∆ 1 with the same meaning as in [1], i.e.…”

Section: Definition Of the Model And The Cvm Pair Approximationmentioning

confidence: 99%

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A cluster variation approach to the random-anisotropy Blume-Emery-Griffiths model

Buzano

Maritan

Pelizzola

1994

J. Phys.: Condens. Matter

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The random-anisotropy Blume-Emery-Griffiths model, which has been proposed to describe the critical behavior of 3 He-4 He mixtures in a porous medium, is studied in the pair approximation of the cluster variation method extended to disordered systems. Several new features, with respect to mean field theory, are found, including a rich ground state, a nonzero percolation threshold, a reentrant coexistence curve and a miscibility gap on the high 3 He concentration side down to zero temperature. Furthermore, nearest neighbor correlations are introduced in the random distribution of the anisotropy, which are shown to be responsible for the raising of the critical temperature with respect to the pure and uncorrelated random cases and contribute to the detachment of the coexistence curve from the λ line.

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Section: Definition Of the Model And The Cvm Pair Approximationmentioning

confidence: 99%

“…The main features are the disappearance of the tricritical point present only in the pure 3 He-4 He system [6] and superfluidity in two coexisting phases, one rich in 3 He and the other in 4 He. Recent experiments [7] have confirmed the above qualitative picture.…”

Section: Introductionmentioning

confidence: 99%

A cluster variation approach to the random-anisotropy Blume-Emery-Griffiths model

Buzano

Maritan

Pelizzola

1994

J. Phys.: Condens. Matter

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“…The second sum is taken over the N spins on a D-dimensional lattice. The case where S = 1 has been extensively studied by several approximate techniques in two-and three-dimensions and its phase diagram is well established [29][30][31][32][33][34][35]. The case S > 1 has also been investigated according to several procedures [36][37][38][39][40][41][42].…”

Section: Model and Simulationmentioning

confidence: 99%

“…The BlumeCapel Model is a generalization of the standard Ising model [28] and was originally proposed for spin-1 to account for first-order phase transition in magnetic systems [29,30]. The Hamiltonian can be written as…”

Section: Model and Simulationmentioning

confidence: 99%

Critical behavior of the spin-3/2 Blume-Capel model on a random two-dimensional lattice

Lima¹,

Plascak²

2006

Braz. J. Phys.

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We investigate the critical properties of the spin-3/2 Blume-Capel model in two dimensions on a random lattice with quenched connectivity disorder. The disordered system is simulated by applying the cluster hybrid Monte Carlo update algorithm and re-weighting techniques. We calculate the critical temperature as well as the critical point exponents γ/ν, β/ν, α/ν, and ν. We find that, contrary of what happens to the spin-1/2 case, this random system does not belong to the same universality class as the regular two-dimensional ferromagnetic model.

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“…The BEG Model or spin-1 Ising Model, introduced by Blume, Emery and Griffiths to describe the behavior of a 3 He − 4 He mixture [21], has the Hamiltonian (without external field)…”

Section: Other Fixed Pointsmentioning

confidence: 99%

Minimalistic real-space renormalization of Ising and Potts Models in two dimensions

2015

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We introduce and discuss a real-space renormalization group (RSRG) procedure on very small lattices, which in principle does not require any of the usual approximations, e.g., a cut-off in the expansion of the Hamiltonian in powers of the field. The procedure is carried out numerically on very small lattices (4 × 4 to 2 × 2) and implemented for the Ising Model and the q = 3, 4, 5-state Potts Models. Nevertheless, the resulting estimates of the correlation length exponent and the magnetization exponent are typically within 3-7% of the exact values. The 4-state Potts Model generates a third magnetic exponent, which seems to be unknown in the literature. A number of questions about the meaning of certain exponents and the procedure itself arise from its use of symmetry principles and its application to the q 5 Potts Model. =

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Ising Model for theλTransition and Phase Separation inHe3-
M. Blume
¹
,
V. J. Emery
²
,
Robert B. Griffiths
³

Cited by 1,534 publications

References 13 publications

A cluster variation approach to the random-anisotropy Blume-Emery-Griffiths model

A cluster variation approach to the random-anisotropy Blume-Emery-Griffiths model

Critical behavior of the spin-3/2 Blume-Capel model on a random two-dimensional lattice

Minimalistic real-space renormalization of Ising and Potts Models in two dimensions

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Ising Model for theλTransition and Phase Separation inHe3-M. Blume1, V. J. Emery2, Robert B. Griffiths3

Cited by 1,534 publications

References 13 publications

A cluster variation approach to the random-anisotropy Blume-Emery-Griffiths model

A cluster variation approach to the random-anisotropy Blume-Emery-Griffiths model

Critical behavior of the spin-3/2 Blume-Capel model on a random two-dimensional lattice

Minimalistic real-space renormalization of Ising and Potts Models in two dimensions

Contact Info

Product

Resources

About

Ising Model for theλTransition and Phase Separation inHe3-
M. Blume
¹
,
V. J. Emery
²
,
Robert B. Griffiths
³