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Effective mean-field theory based on cumulant expansion in treating classical Heisenberg model on stacked triangular lattice. (English) Zbl 1220.82032

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
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