‘‘Spiraling’’ algorithm: Collective Monte Carlo trial and self-determined boundary conditions for incommensurate spin systems

Abstract

To study incommensurate spin systems, we employ a collective Monte Carlo trial that enables the system to choose its own boundary conditions. The method is tested on a generalization of the 2D fully frustrated triangular lattice of XY spins. Even for small sizes of our model system, the bulk value for the pitch is obtained. Convergence as a function of size is far better than can be obtained with free or periodic boundary conditions. Moreover, this approach yields the temperature dependence of the pitch in the modulated phase. The spiral-to-antiferromagnetic phase transition appears to be continuous and a Lifshitz point occurs at finite temperature.