Analytic average magnetization expression for the body centered cubic Ising lattice

Abstract

Recently we have performed large-scale average magnetization studies of the Ising model for the square, honeycomb, triangular, and simple cubic lattice. We want to complement those studies with the structurally more complicated body-centered cubic lattice Ising model in this paper. We have relevantly calculated the order parameter or average magnetization expression for the body-centered cubic Ising lattice based on the recently developed interrelation, given by σ0,i = tanh[K(σ1,i + σ2,i + • • • + σz,i) + H] . We will use the same conjectures for the odd spins correlation functions as in our previous works. The mathematical forms of the odd spin correlation functions will be eventually elucidated by some physical discussions. We have seen that the obtained average magnetization expression with the numerical data for the body-centered cubic lattice Ising model is in good agreement.

Relevant Analytic Spontaneous Magnetization Relation for the Face-Centered-Cubic Ising Lattice

“…We now proceed by introducing the heuristic OSCM expression as given in Refs. [79][80][81] in the form of…”

“…in which k on the subscript is an odd number that refers to the order of the odd-correlations, r labels the groups, β denotes the critical exponent, and λ k,r may take 0 ≤ λ k,r ≤ 1 values by definition [79][80][81]. Applying Eq.…”

“…Considering the spontaneous magnetization of the 3D Ising model, a most recent approach in the context of effective field theory [53] given by Kaya [79][80][81] has successively led to deriving relevant analytic spontaneous magnetization relations for the simple-cubic (SC) and body-centered-cubic Ising lattices. This has been achieved by proposing a heuristic odd-spin correlation magnetization (OSCM) relation by means of associating it to the Callen-Suzuki [64,82,83] identity.…”