Developing Cluster Algorithms for the ANNNI Model

Presenter

Shane Alexander Keiser

Campus

UMass Amherst

Sponsor

Jonathan Lee Machta, Department of Physics, UMass Amherst

Schedule

Session 4, 2:30 PM - 3:15 PM [Schedule by Time][Poster Grid for Time/Location]

Location

Poster Board A86, Campus Center Auditorium, Row 5 (A81-A100) [Poster Location Map]

Abstract

The Axial Next-Nearest Neighbor Ising (ANNNI) model is a variant of the Ising model, which is a mathematical model of ferromagnetism in statistical physics. Ferromagnetism is a property that allows materials to become permanent magnets. The ANNNI model describes a lattice of discrete variables called 'spins', which can take 'up' (+1) or 'down' (-1) states. Spins are coupled through attractive nearest neighbor interactions as in the Ising model; there is also coupling through repulsive next-nearest neighbor interactions along one axis. We do numerical simulations of this model, where the longer range interactions introduce frustration in the lattice resulting in a translational symmetry which is characteristic of crystals.

It is of interest to determine the macroscopic behavior of the system over time, while varying coupling parameters, and external parameters such as temperature. There are also differences in behavior depending on the size of the lattice. Through the simulation, we can determine properties of the system that are derived from its fluctuating energy and magnetization levels, and the time to reach a state of equilibrium.

In this independent study we use C++ to write algorithms, such as the Metropolis-Hastings and Wolff algorithms for the Ising model, as well as more detailed cluster methods for the ANNNI model. These algorithms utilize randomness to greatly enhance simulation efficiency. We collect data from these simulations, which is then analyzed and illustrated using Python scripts. In particular, this study emphasizes the extent to which these algorithms describe systems, as well as the algorithms' time efficiency.

Keywords

Theory, Computing, Simulation, Modelling, Phenomena

Research Area

Physics and Nanotechnology

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