Abstract
We have considered a classical spin system, consisting of n-component unit vectors (n = 2, 3), associated with a semi-infinite lattice in one dimension {uk, k ∈ N+}, and interacting via inhomogeneous pair potentials, anisotropic in spin space, and of the long-range ferromagnetic form [Formula: see text] here ∊ is a positive constant setting energy and temperature scales (i.e. T* = k B T/∊), a > 0, b ≥ 0, and the symbols uj,α denote Cartesian components of the spins. On the basis of available theoretical results, one can prove the existence of an ordering transition at a finite temperature for n ≥ 2, b = 0, as well as upper and lower bounds on the transition temperatures. We have studied the two cases n = 2, 3, b = 0, by computer simulation, and made a comparison with the Mean Field treatment.
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