The phase diagrams of a spin-1 transverse Ising model

Correlation identities and rigorous upper bounds on the critical temperature for the spin-1 Blume–Capel model on a Kagome lattice

“…By reducing the value of D, we have a decrease of T c . Moreover, at zero temperature, the first-order transition line ends at the point D c /J = −z/2, where z is the coordination number of the lattice [4][5][6].…”

“…The spin-1 Blume-Capel model was studied by a variety of methods such as mean-field approximation (MFA) [1,2], effective-field approximation (EFA) [4][5][6][7][8][9], the Bethe lattice approximation [10], series expansion method (SE) [11,12], cluster variation method (CVM) [13], Monte Carlo (MC) simulations [14][15][16][17], renormalization-group (RG) method [18,19] and rigorous inequality correlation function [20][21][22]. Most of these studies were done on hexagonal and rectangular lattices.…”

“…Recently, an expression for the free energy was calculated numerically for the spin-1 transverse Ising model on a honeycomb lattice [4] using EFA and it was used to obtain the first-order transition line. The phase diagram in the (k B T /J × D/J) plane was found for all values of anisotropy parameter.…”

“…From the correlation identities we obtain results for the magnetization, phase transitions lines and tricritical points with the application of the MFA and the EFA which, as has been said previously, includes the effects of autocorrelations through the usage of the van der Waerden identities and provide results that are superior to those obtained within the MFA. In the application of the EFA a free-energy functional [4,6,5] was used to obtain the line of first order transitions. We remark that the results obtained improve over the one-site MFA and the one-site EFA because the five-site cluster contains more correlations than the one-site cluster.…”

An introduced effective-field theory study of spin-1 transverse Ising model with crystal field anisotropy in a longitudinal magnetic field

“…The effect of a longitudinal crystal field on the phase transitions in spin-3/2 and spin-2 transverse Ising model has been also examined for both honeycomb and square lattices by using the EFT with correlations [17,18]. More recently, within the basis of EFT and MFT, Miao et al [19] have studied the phase diagrams of a spin-1 transverse Ising model for a honeycomb lattice. They have obtained the first-order transition lines by comparing the Gibbs free energy.…”