Computer Simulation Study of Classical Spin Models in Two Dimensions with Long-Range Ferromagnetic Interactions Anisotropic in Spin Space

Abstract

We have considered a classical spin system, consisting of 3-component unit vectors, associated with a two-dimensional lattice {uk, k ∈ Z2}, and interacting via a translationally invariant pair potential, of the long-range ferromagnetic form, anisotropic in spin space [Formula: see text] here a ≥ 0, b ≥ 0, σ > 2, ∊ is a positive constant setting energy and temperature scales (i.e. T*=kBT/∊), xj denotes dimensionless coordinates of lattice sites, and uj,α cartesian spin components; our discussion has been specialized to the extreme, O(2)-symmetric, case 0=a < b. When 2 < σ < 4, the potential model can be proven to support an ordering transition taking place at finite temperature; on the other hand, when σ ≥ 4 a Berezinskiǐ–Kosterlitz–Thouless-like transition takes place. Two potential models defined by σ=3 and σ=4, respectively, have been characterized quantitatively by Monte Carlo simulation. For σ=3, comparison is also reported with other theoretical treatments, such as Molecular Field and Two Site Cluster approximations.