ISSN:
1089-7550
Source:
AIP Digital Archive
Topics:
Physics
Notes:
The application to incommensurate spin systems of the Monte Carlo method has been an ongoing problem for many years. We resolve it by employing a spiraling algorithm that enables the system to choose its own boundary conditions (i.e., its pitch Δ). The model considered is a modification of the 2D fully frustrated triangular lattice of XY spins: all horizontal bonds are multiplied by a factor η.1,2 This system has two ordered phases: spiral and antiferromagnet. In the spiral phase, even for small sizes of the system, the algorithm gives the bulk value for the pitch; convergence as a function of size is far better than can be obtained with free or periodic boundary conditions. Moreover, the algorithm yields the temperature dependence of the incommensurate pitch in the spiral phase. The spiral-to-antiferromagnetic phase transition is continuous and a Lifshitz point occurs at finite temperature. The spiral-to-antiferromagnetic phase transition does not appear in the specific heat Cv or the spin stiffness ρyy along y, but it does appear in the helicity ψhel (a measure of the sense of twist of the spiral), the helicity susceptibility χhel, and in the spin stiffness ρxx along x.3 This latter quantity cannot be computed by the usual procedures when the boundary conditions are permitted to vary, but it is inversely proportional to χΔ, the fluctuation-determined susceptibility of the pitch.3
Type of Medium:
Electronic Resource
URL:
http://dx.doi.org/10.1063/1.353636
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