Phase diagrams and tricritical effects in the beg model

Ananikian, N. S.; Avakian, Artjom; Измаилян, Н. Ш.

doi:10.1016/0378-4371(91)90391-o

Cited by 60 publications

(49 citation statements)

References 22 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…The study of the BEG model in the canonical ensemble has been performed in the past on a Bethe lattice [34,35]. In this case, the model can be exactly solved using recursive relations for the partition function.…”

Section: Discussionmentioning

confidence: 99%

Complete analysis of ensemble inequivalence in the Blume-Emery-Griffiths model

et al. 2017

View full text Add to dashboard Cite

We study inequivalence of canonical and microcanonical ensembles in the mean-field BlumeEmery-Griffiths model. This generalizes previous results obtained for the Blume-Capel model. The phase diagram strongly depends on the value of the biquadratic exchange interaction K, the additional feature present in the Blume-Emery-Griffiths model. At small values of K, as for the Blume-Capel model, lines of first and second order phase transitions between a ferromagnetic and a paramagnetic phase are present, separated by a tricritical point whose location is different in the two ensembles. At higher values of K the phase diagram changes substantially, with the appearance of a triple point in the canonical ensemble which does not find any correspondence in the microcanonical ensemble. Moreover, one of the first order lines that starts from the triple point ends in a critical point, whose position in the phase diagram is different in the two ensembles. This line separates two paramagnetic phases characterized by a different value of the quadrupole moment. These features were not previously studied for other models and substantially enrich the landscape of ensemble inequivalence, identifying new aspects that had been discussed in a classification of phase transitions based on singularity theory. Finally, we discuss ergodicity breaking, which is highlighted by the presence of gaps in the accessible values of magnetization at low energies: it also displays new interesting patterns that are not present in the Blume-Capel model.

show abstract

Section: Discussionmentioning

confidence: 99%

Complete analysis of ensemble inequivalence in the Blume-Emery-Griffiths model

et al. 2017

View full text Add to dashboard Cite

show abstract

“…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%

“…[12,13] and use recursion relations to derive the tricritical point of the BEG model on the Bethe lattice with equal couplings for the two nearest-neighbour interaction terms. This is compared to a saddle-point calculation on regular random graphs in Section 3.…”

Section: Introductionmentioning

confidence: 99%

Potts models with invisible states on general Bethe lattices

Ananikian¹,

Izmailyan²,

Johnston³

et al. 2013

J. Phys. A: Math. Theor.

View full text Add to dashboard Cite

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]

show abstract

“…It cannot be obtained by directly evaluating the logarithm of the partition function in which the contribution from the outside of this region is not negligible and as result the system exhibits an unusual type of phase transitions without long-range order [11,12,13]. Recently, a method for the surface independent free energy calculation is presented [14,15]. The free energy f ✷ per plaquette of our model is expressed as…”

Section: The Bethe-like Latticementioning

confidence: 99%