Metropolis Monte Carlo and Wang-Landau Simulations of Tricriticality in Crossed Ising Chains

ORAL

Abstract

We explore the phase diagram of Ising spins on one-dimensional chains which criss-cross in two perpendicular directions and which are connected by interchain couplings. This system is of interest as a simpler, classical analog of a quantum Hamiltonian which has been proposed as a model of magnetic behavior in Nb$_{12}$O$_{29}$ and also, conceptually, as a geometry which is intermediate between one and two dimensions. Using mean field theory as well as Metropolis Monte Carlo and Wang-Landau simulations, we locate quantitatively the boundaries of four ordered phases. Each becomes an effective Ising model with unique effective couplings at large interchain coupling. Away from this limit we demonstrate non-trivial critical behavior, including tricritical points which separate first and second order phase transitions. Finally, we find that the crossover of the magnetization critical exponent from the Ising to tricritical Ising value shows an unusual non-monotonic behavior.

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Authors

  • Tyler Cary

    University of California, Davis

  • Ethan Anderes

    UC Davis, Lawrence Berkeley National Lab - ALS, National Institute of Standards and Technology - NCNR, Univ of California - Davis, University of California, Davis, California State University, Long Beach, University of California, Irvine, University of California, Merced, UC Merced, U Central Florida, Paul Scherrer Institute, Paul Scherrer Institute in Switzerland, Hartnell Comm Coll, University of Michigan, University of Nevada, Reno, National Security Technologies LLC, Livermore, California, Humboldt State University, Stanford University, San Diego State Univ, Institute of Mathematical Problems of Biology, Eindhoven University of Technology, University Of Nevada Reno, Univ of Nevada - Reno, University of Chicago, Physics Department of the University of Nevada, Reno, NV, USA, Institute for Academic Initiatives, PPC and Graduate School of Engineering, Osaka University, Joint Institute for High Temperatures, PPC and Graduate School of Engineering, Osaka University, Institute for Academic Initiatives, Joint Institute for High Temperatures, National Institute of Standards and Technology, Gaithersburg, MD, Department of Physics, UC Davis, Department of Physics & Astronomy, Univeristy of California Irvine, 92697, Department of Chemistry and of Physics, Univeristy of California Irvine, 92697, Department of Condensed Matter Physics, Weizmann Institute of Science, Rehovot, Israel 76100, Einstein Centre for Local-Realistic Physics, Cal State Long Beach, University of nevada, Reno, Nicolaus Copernicus University, Torun, Poland, University of Maryland, CERN, Univ of California, Davis

  • Ethan Anderes

    UC Davis, Lawrence Berkeley National Lab - ALS, National Institute of Standards and Technology - NCNR, Univ of California - Davis, University of California, Davis, California State University, Long Beach, University of California, Irvine, University of California, Merced, UC Merced, U Central Florida, Paul Scherrer Institute, Paul Scherrer Institute in Switzerland, Hartnell Comm Coll, University of Michigan, University of Nevada, Reno, National Security Technologies LLC, Livermore, California, Humboldt State University, Stanford University, San Diego State Univ, Institute of Mathematical Problems of Biology, Eindhoven University of Technology, University Of Nevada Reno, Univ of Nevada - Reno, University of Chicago, Physics Department of the University of Nevada, Reno, NV, USA, Institute for Academic Initiatives, PPC and Graduate School of Engineering, Osaka University, Joint Institute for High Temperatures, PPC and Graduate School of Engineering, Osaka University, Institute for Academic Initiatives, Joint Institute for High Temperatures, National Institute of Standards and Technology, Gaithersburg, MD, Department of Physics, UC Davis, Department of Physics & Astronomy, Univeristy of California Irvine, 92697, Department of Chemistry and of Physics, Univeristy of California Irvine, 92697, Department of Condensed Matter Physics, Weizmann Institute of Science, Rehovot, Israel 76100, Einstein Centre for Local-Realistic Physics, Cal State Long Beach, University of nevada, Reno, Nicolaus Copernicus University, Torun, Poland, University of Maryland, CERN, Univ of California, Davis