First-order directional ordering transition in the three-dimensional compass model

2014/06/30 by Max H. Gerlach, Wolfhard Janke · 7 citations
Earth and Planetary Sciences · Mathematics · Physics and Astronomy · #Artificial intelligence #Boundary value problem #Cluster (spacecraft) #Combinatorics #Compass #Computer science #Condensed matter physics #Embedding #High-pressure geophysics and materials #Histogram #Hybrid Monte Carlo #Markov chain Monte Carlo #Mathematics #Monte Carlo method #Order (exchange) #Parallel tempering #Periodic boundary conditions #Phase transition #Physics #Physics of Superconductivity and Magnetism #Quantum mechanics #Simple (philosophy) #Statistical physics #Statistics #Theoretical and Computational Physics #cond-mat.stat-mech #cond-mat.str-el

paper · pdf · doi:10.1103/physrevb.91.045119

published in Physical Review B 91(4) (American Physical Society) · 8.5 pages, 7 figures, 2 tables

arxiv created 2015/01/16 · openalex publication_date 2015/01/16 · arxiv updated 2015/01/19 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05

Abstract

We study the low-temperature properties of the classical three-dimensional compass or t_2g orbital model on simple-cubic lattices by means of comprehensive large-scale Monte Carlo simulations. Our numerical results give evidence for a directionally ordered phase that is reached via a first-order transition at the temperature T₀=0.098\phantom\rule0.16em0ex328(3)J/k_B. To obtain our results, we employ local and cluster update algorithms, parallel tempering and multiple histogram reweighting as well as model-specific screw-periodic boundary conditions, which help counteract severe finite-size effects.

Citations

• Monte Carlo simulations of the directional-ordering transition in the two-dimensional classical and quantum compass model
• Unveiling the Nature of Three-Dimensional Orbital Ordering Transitions: The Case ofegandt2gModels on the Cubic Lattice
• Equation of State Calculations by Fast Computing Machines
• Re-examining the directional-ordering transition in the compass model with screw-periodic boundary conditions
• Multicanonical analysis of the plaquette-only gonihedric Ising model and its dual
• Orbital order in classical models of transition-metal compounds
• Topologically Decoherence-Protected Qubits with Trapped Ions