Theoretical and Computational Ising Model Studies: Work and Time Costs of Information Erasure

ORAL

Abstract

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.

–

Authors

  • Francis Cavanna

    University of Dallas

  • Qiye Zheng

    Santa Fe Institute, Baylor University, University of Texas at Dallas, Department of Chemistry, The University of Texas at Austin, Jozef Stefan Institute, Texas A&M University-Commerce, Commerce, Texas 75429, Cyclotron Institute, Texas A&M University, College Station, Texas 77843, Texas A&M University, Department of Physics, Texas State University, Department of Physics, Baylor University, University of Texas at El Paso, Univ of Texas, El Paso, University of Science and Technology of China, The University of Texas at Dallas, Faculty, None, Southwestern University, Texas State University, Texas A&M University - Commerce, UT Southwestern Medical Center, National High Magnetic Field Laboratory, The Cyclotron Institute at Texas A&M University, Department of Biological Sciences, Texas State Univ-San Marcos, The University of Texas at Dallas, Richardson, Texas 75080, King Abdullah University of Science and Technology, Univ of Texas, Dallas, N.Chiao Tung U., UT Dallas, Inorganic Chemistry and Catalysis Group, Utrecht University, Electrical & Computer Engineering, Baylor University, Department of Materials Science and NanoEngineering, Rice University, University of Texas at Arlington, University of Chicago, The University of Mississippi, Astronomical Observatory, Warsaw University, Nicolaus Copernicus Astronomical Centre, Polish Academy of Sciences, Rochester Institute of Technology, California Institute of Technology, University of Houston, NASA-GSFC and UMBC, MD, Virginia Tech, VA, Texas Christian University, The University of Texas at San Antonio, Department of Physics, Teivecca Nazarene University, Weatherford College, Air Force Research Laboratory, Sensors Directorate, WPAFB, OH, USA, Air Force Research Laboratory, Directed Energy Directorate, KAFB, NM, US, Department of Physics & Astronomy, University of Texas at San Antonio TX, USA, University of Arizona, University of North Carolina at Chapel Hill, Stanford University, Harvard Center for Astrophysics, Texas A\&M University, UTSW, University of Illinois at Urbana-Champaign, Urbana, Illinois 61801, Boston College, Chestnut Hill, Massachusetts 02467, Naval Research Laboratory, Washington, D.C. 20375