APS -Joint Fall 2017 Meeting of the Texas Section of the APS, Texas Section of the AAPT, and Zone 13 of the Society of Physics Students- Event - Theoretical and Computational Ising Model Studies: Work and Time Costs of Information Erasure

摘要

An Ising model is used to test whether computational operations optimize at critical points, which are specific values dividing two distinct phases of a statistical system. The Ising lattice takes a bit value of $1$ for an average magnetization (or net magnetization) greater than 0 ($M > 0$), and a bit value of 0 if ($M < 0$). The simulation is varied through multiple values of $k_B T$ to replicate the phase transition at the critical point $k_B T = 2.269$. Next, the minimum values of the required external magnetic field $h$ and the associated work consumption are found for performing the boolean computational operation RESET TO ZERO on a 4x4 Ising lattice with the following erasure success rates: $0.75,;0.80,;0.85,;0.90$, and $0.95$. Finally, a time-evolving Ising lattice simulation is performed for the 4x4 lattice to measure the time required to drive the net magnetization to 0 from an initial value of 1 with and without negative external magnetic fields. All programs use Jupyter Notebooks and Python 3.6.1. The work required for a RESET TO ZERO operation for any arbitrary tolerance is found to approach 0 as $k_B T$ approaches 0, but the time for the operation with the minimum required external magnetic field appears to go to infinity.