The anisotropic Ising superantiferromagnet on a simple cubic lattice in the presence of a magnetic field: Effective-field theory analysis

Multicritical behavior of the two-dimensional transverse Ising metamagnet in a longitudinal magnetic field

“…Although these approaches agree with the overall phase diagram in two dimensions, LCA [15] and EFT [20] approaches produce a reentrant be-havior in the first-order transition line. The same reentrant behavior is obtained for the three-dimensional model by the EFT with four spins [22].…”

“…Ω = 0, on anisotropic square lattices has been investigated by using a modified mean-field theory, in which the intrachain interaction is treated exactly and the interactions between chains are taken into account in a mean-field way (linear chain approximation -LCA) [12][13][14][15][16]. Several other approaches, such as usual mean-field approximation (MFA) [17][18][19], effective-field theory (EFT) [20][21][22], mean-field renormalization group (MFRG) [23], effective-field renormalization group (EFRG) [24], Monte Carlo simulations (MC) [25][26][27][28][29], and high-temperature series expansion (SE) [30] have also been applied to this classical model. Although these approaches agree with the overall phase diagram in two dimensions, LCA [15] and EFT [20] approaches produce a reentrant be-havior in the first-order transition line.…”

“…from which we get the second-order transition lines when a 2 = 0 and a 4 > 0, and the tricritical point when a 2 = 0, a 4 = 0 and a 6 > 0 (see, for instance, Refs. [22,34]). In present case, a 0 is not important for our purposes, so the a 2 , a 4 , and a 6 coefficients can be written as…”