COMPUTER SIMULATION STUDY OF LATTICE SPIN MODELS IN ONE DIMENSION WITH LONG-RANGE INHOMOGENEOUS INTERACTIONS POSSESSING O(2) SYMMETRY

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, in general 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. For some specific values of the two parameters a and b, and on the basis of available theoretical results, one can prove the existence of an ordering transition taking place at finite temperature, and obtain rigorous upper and lower bounds on the transition temperatures. This holds, for example, when n = 2, 3, a > b = 0 (the models studied in our previous paper), as well as for n = 2, a = b > 0 and n = 3, b > a = 0, where a continuous O(2) symmetry of the interaction is involved. We have studied these two latter cases by computer simulation, and made comparison with mean-field treatment; simulation results show a broad qualitative similarity between the four models, and a closer, quantitative one, between pairs of models with the same number of spin components, especially for n = 2.