Monte Carlo simulation of a one dimensional classical Heisenberg model with long range interactions

Abstract

We have studied a classical system, consisting of three dimensional unit vectors associated with a one dimensional lattice {u _k|k ∈ Z} and interacting via the translationally invariant pair potential

This potential model has been proven rigorously to possess a ferromagnetically ordered phase at low but finite temperature. We also consider the pair interaction defined by

the two potential models have the same partition function, and essentially the same structural properties, thus V' possesses a low-temperature transition to an anti-ferromagnetically ordered phase. In turn, V' can be regarded as an extreme case of a nematogenic lattice model, whose structural properties can still be evaluated under V. The system was characterized quantitatively by Monte Carlo simulation, whose results are compatible with a second order transition at T*_c(=kT_c/ε) of 1·48 ± 0·02. Comparison with molecular field and spherical model treatments is also reported; the former, but not the latter, agrees reasonably with the simulation results.