Phase diagrams of the Blume-Emery-Griffiths model: real-space renormalization group investigation and finite size scaling analysis

Bakchich, A.; Benyoussef, A.; Touzani, M.

doi:10.1016/0378-4371(92)90214-b

Cited by 17 publications

(12 citation statements)

References 28 publications

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“…Using the histogram extrapolation technique, we have obtained the temperature dependence of this slope for the spin fluid model. The results yield the estimate y 3 = 0.83 (5), which agrees to within error with the exact conjecture.…”

Section: The Spin Fluid Modelsupporting

confidence: 81%

“…As with the 2d spin fluid model, the symmetry of the configurational energy under spin sign reversal implies that the tricritical point lies in the symmetry plane H = 0. Previous MCRG [15,16] investigations place the tricritical point of the 2d Blume-Capel model at K B T t /J = 0.609(3), D t = 1.965 (15), while a more recent transfer matrix study [9] gives K B T t /J = 0.610(5), D t = 1.965 (5). Using these estimates as an initial guide, we performed extensive Monte Carlo simulations of the model using a vectorised Metropolis algorithm on a Cray-YMP.…”

Section: B the 2d Blume-capel Modelmentioning

confidence: 99%

“…For tricritical phenomena, the highest dimension in which non-classical behaviour can be observed is d = 2 [1]. Consequently, 2d tricritical phenomena has been the subject of a large number of previous investigations, employing a wide variety of techniques, including series expansions [2], mean-field theory [3], renormalisation group (RG) [4][5][6][7][8], transfer matrix [9][10][11][12], Monte Carlo simulations [13,14] and Monte Carlo RG methods [15][16][17]. To date, however, this interest has focused almost exclusively on lattice-based spin models such as the Blume-Capel model or the spin-1 2 next-nearest-neighbour Ising model.…”

Section: Introductionmentioning

confidence: 99%

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Tricritical universality in a two-dimensional spin fluid

1996

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Monte Carlo simulations are used to investigate the tricritical point properties of a 2d spin fluid. Measurements of the scaling operator distributions are employed in conjunction with a finite-size scaling analysis to locate the tricritical point and determine the directions of the relevant scaling fields and their associated tricritical exponents. The scaling operator distributions and exponents are shown to match quantitatively those of the 2d Blume-Capel model, confirming that both models belong to the same universality class. Mean-field calculations of the tricritical point properties are also compared with the simulation measurements.Comment: 9 pages Revtex, 7 ps figures (uuencoded). Phys. Rev. E. (in press). Paper also available from http://moses.physik.uni-mainz.de/~wilding/home_wilding.htm

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Section: The Spin Fluid Modelsupporting

confidence: 81%

Section: B the 2d Blume-capel Modelmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Tricritical universality in a two-dimensional spin fluid

1996

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“…Another interesting observation we have is that for K ≤ −1 the two ensembles are equivalent. Attractive BEG model has been well studied and we find results similar to as reported in the earlier studies [1,[12][13][14][15][16][17][18][19][20][21]. Since we looked at the phase diagram in the (T − ∆ − H) space, we found a non-monotonic behaviour of the wings in terms of temperature as K becomes greater than K = 1.…”

Section: Introductionsupporting

confidence: 88%

“…For larger value of K, the continuous transition line terminates on the first order line at a critical end point(CEP), and the TCP disappears. The phase diagram has been well studied using various techniques like mean-field [1,[12][13][14][15], renormalization group [16,17]), Monte-Carlo simulation [18], cluster variation [19], Bethe lattice [20], high-temperature series expansion [21] etc.…”

Section: Introductionmentioning

confidence: 99%

Phase diagram of the repulsive Blume-Emery-Griffiths model in the presence of external magnetic field on a complete graph

Mukherjee,

Sadhu

2020

Preprint

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For the repulsive Blume-Emery-Griffiths model the phase diagram in the space of three fields, temperature (T ), crystal field (∆) and magnetic field (H), is computed on a fully connected graph, in the canonical and microcanonical ensembles. When the strength of the biquadratic interaction (K) is low, there exists a tricritical point where the three critical lines meet. As K decreases, new multicritical points like the critical end point and bicritical end point arise in the (T, ∆) plane. For K > −1, we observe that the two critical lines in the H plane and the multicritical points are different in the two ensembles. At K = −1, the two critical lines in the H plane disappear and as K decreases further, we see no phase transition in the H plane. Exactly at K = −1 the two ensembles become equivalent. Beyond that for all K < −1, there are no multicritical points and there is no ensemble inequivalence in the phase diagram. We also study the transition lines in the H plane for positive K i.e. for attractive biquadratic interaction. We find that the transition lines in H plane are not monotonic in temperature for large positive K.

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