Effective‐field renormalization‐group approach for quenched site‐dilute ising models

Bobák, A.; Jaščur, M.; Mockovčiak, S.

doi:10.1002/pssb.2221830223

Cited by 4 publications

(4 citation statements)

References 19 publications

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“…We have found that for p = 1 (pure system) kBTJJ = 2.9557 and the critical concentration p c at which T, reduces to zero is given by pc = 0.4517. This value for p c represents an improvement to the two-spin cluster approximation without nearest-neighbour correlations of pc = 0.4294 [3,4] and is somewhat closer to the best value ofp, = 0.590 obtained by the series expansion method [5]. The value of E,(P) decreases from the value E, = 0.3591 at p = 1 to the critical value E, = 0.1791 at p = p c (see Fig.…”

Section: Role Of Nearest-neighbour Correlations In the Site-diluted Ssupporting

confidence: 76%

Role of nearest‐neighbour correlations in the site‐diluted spin‐1/2 Ising model

Bobák

Jaščur

1995

Physica Status Solidi (b)

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For many years now there has been extensive study of the second-order phase transition in the diluted Ising model. The points of interest in the theoretical and the experimental studies of such disordered magnets are the concentration dependence of the critical temperature and the value of the critical concentration of magnetic atoms below which the system will not exhibit a transition to magnetic order. Due to the fact that for both two-and three-dimensional systems no exact solution is known for the model, the presently available results are all based on theoretical approximations or computer simulations.In particular, among the successful methods used to tackle the problem, there have been the one-[ l , 21 and two-spin [3] cluster approximations. However, the results of [3] are based on the decoupling approximation that neglects the correlations not only between nextnearest neighbours but also between nearest neighbours. Therefore, further improvement to the theory will result if at least nearest-neighbour correlations are taken into account. This has been illustrated in the present note for the square lattice.The Hamiltonian of our system is given by where (i, j ) runs over all nearest-neighbour pairs of spins, ti = l(0) if the site i is occupied (unoccupied) by a magnetic atom and J is the exchange interaction.According to [3], we can obtain an exact equation for a pair of neighbouring spins as follows: (( t j ( 1 -ti) k ' = ' fi' 1 Bk'))c tanh T I x=o,y=o ') Moyzesova 16, 041 54 Koiice, Slovakia.

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Section: Role Of Nearest-neighbour Correlations In the Site-diluted Ssupporting

confidence: 76%

Role of nearest‐neighbour correlations in the site‐diluted spin‐1/2 Ising model

Bobák

Jaščur

1995

Physica Status Solidi (b)

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“…Below a critical occupancy fraction this model does not experience a phase transition; p c Ϸ0.27 to 0.31. 20 If no spinodal decomposition is carried out, our model corresponds to the dilute Ising model with an occupancy fraction of 50%, well above p c , and it will have a phase transition. For larger pore sizes ͑increasing periods of spinodal decomposition͒ the connectivity of the spin-spin interactions is increased and thus we expect the phase transition to persist.…”

Section: Nature Of Demixing Phase Transition In a Porous Mediummentioning

confidence: 99%

Equilibrium phase transitions in a porous medium

1996

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Static critical phenomena of a three-dimensional Ising model confined in a porous medium made by spinodal decomposition have been studied using large-scale Monte Carlo simulations. We thus examine the influence of the geometry of Vycor-like materials on phase transitions. No surface interactions ͑preference of the Vycor-like material for one phase above the other͒ are taken into account. We find that the critical temperature depends on the average pore size D as T c (D)ϭT c (ϱ)Ϫc/D. The critical exponents are independent of pore size: we find ϭ0.8Ϯ0.1, ␥ϭ1.4Ϯ0.1, ␤ϭ0.65Ϯ0.13. No divergence is observed for the specific heat, indicating ␣р0. All data for all pore sizes can be collapsed well with the scaling function for the magnetic susceptibility L Ϫ␥/ ϭ˜(tL 1/ ), where tϭT/T c (D)Ϫ1. These critical phenomena are consistent with those computed for the randomly site-diluted Ising model. Experimental realizations of our numerical experiments are discussed.

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“…The other would be based on invariance of scale, where the Eqs. (30) and (32) are equivalents, i.e.,…”

Section: F Mfrg-12 Approachmentioning

confidence: 99%

“…These two methods have been applied to a variety of magnetic spin models in obtaining of the critical properties of classical XY and Heisenberg models [30], critical behavior of two-and three-dimensional ferromagnetic and antiferromagnetic spin-ice systems [31], quenched site-dilute ising models [32] and to obtain the reduced critical temperature and exponents ν for bi-and threedimensional lattices [33].…”

Section: Introductionmentioning

confidence: 99%

Phase transition induced by an external field in a three-dimensional isotropic Heisenberg antiferromagnet

et al. 2018

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In this paper, we report mean-field and effective-field renormalization group calculations on the isotropic Heisenberg antiferromagnetic model under a longitudinal magnetic field. As is already known, these methods, denoted by MFRG and EFRG, are based on the comparison of two clusters of different sizes, each of them trying to mimic certain Bravais lattice. Our attention has been on the obtention of the critical frontier in the plane of temperature versus magnetic field, for the simple cubic and the body-centered cubic lattices. We used clusters with N = 1, 2, 4 spins so as to implement MFRG-12, EFRG-12 and EFRG-24 numerical equations. Consequently, the resulting frontier lines show that EFRG approach overcomes the MFRG problems when clusters of larger sizes are considered.

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Effective‐field renormalization‐group approach for quenched site‐dilute ising models

Cited by 4 publications

References 19 publications

Role of nearest‐neighbour correlations in the site‐diluted spin‐1/2 Ising model

Role of nearest‐neighbour correlations in the site‐diluted spin‐1/2 Ising model

Equilibrium phase transitions in a porous medium

Phase transition induced by an external field in a three-dimensional isotropic Heisenberg antiferromagnet

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