Yang, Limin; Zhao, Songqing; Zhao, Kun; Fan, Yunxia; Li, P.; Song, Y. Effective mean-field theory based on cumulant expansion in treating classical Heisenberg model on stacked triangular lattice. (English) Zbl 1220.82032 Int. J. Mod. Phys. B 25, No. 6, 833-841 (2011). Summary: An effective mean-field theory based on cumulant expansion is used to deal with antiferromagnetic Heisenberg model on planar triangular lattice. The corrections of expansion are performed to the third order. By using the equation of the mean field condition, curves of internal energy \(E\) specific heat \(C\) staggered helicity \(K\) (order parameter) and the variational ratio of staggered helicity \(X\) are obtained when the proper values of effective external field are achieved. The calculated results showed that there are two phases (which are ordered antiferromagnetic phase and the disordered phase) in the spin system. The first order critical point is \(-kT_{c}/J_{s} = 1.65\), the second is \(-kT_{c}/J_{s} = 1.35\) and the third is \(-kT_{c}/J_{s} = 1.29\), obviously closer to that of Monte Carlo simulation order by order. And also, the analytic expansion curves derived from this method exhibited higher proximity order by order to the Monte Carlo simulation. Such results showed that this method is a useful tool to obtain thermodynamically observables of spin system. MSC: 82B20 Lattice systems (Ising, dimer, Potts, etc.) and systems on graphs arising in equilibrium statistical mechanics 82D40 Statistical mechanics of magnetic materials 82B27 Critical phenomena in equilibrium statistical mechanics 82B44 Disordered systems (random Ising models, random Schrödinger operators, etc.) in equilibrium statistical mechanics Keywords:classical Heisenberg model; mean field; cumulant expansion; antiferromagnetic PDFBibTeX XMLCite \textit{L. Yang} et al., Int. J. Mod. Phys. B 25, No. 6, 833--841 (2011; Zbl 1220.82032) Full Text: DOI References: [1] DOI: 10.1063/1.528650 · Zbl 0722.05057 · doi:10.1063/1.528650 [2] DOI: 10.1143/JPSJ.17.1100 · Zbl 0118.45203 · doi:10.1143/JPSJ.17.1100 [3] DOI: 10.1063/1.1743985 · doi:10.1063/1.1743985 [4] DOI: 10.1016/0370-2693(85)90484-8 · doi:10.1016/0370-2693(85)90484-8 [5] DOI: 10.1016/0370-2693(85)90578-7 · doi:10.1016/0370-2693(85)90578-7 [6] DOI: 10.1103/PhysRevB.63.134419 · doi:10.1103/PhysRevB.63.134419 [7] DOI: 10.1088/0253-6102/17/4/421 · doi:10.1088/0253-6102/17/4/421 [8] DOI: 10.1016/0375-9601(96)00534-8 · doi:10.1016/0375-9601(96)00534-8 [9] DOI: 10.1016/S0375-9601(98)00345-4 · doi:10.1016/S0375-9601(98)00345-4 [10] DOI: 10.1063/1.338936 · doi:10.1063/1.338936 [11] Dagotto E., Series on Advance in Statistical Mechanics 7 pp 43– (1991) [12] DOI: 10.1143/JPSJ.53.1145 · doi:10.1143/JPSJ.53.1145 This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.