Monte Carlo simulations of the directional-ordering transition in the two-dimensional classical and quantum compass model

2008/04/30 by S. C. Wenzel, Sandro Wenzel, Wolfhard Janke · 1 citation
Mathematics · Physics and Astronomy · #Boundary value problem #Critical exponent #Geometry #Ising model #Mathematics #Monte Carlo method #Periodic boundary conditions #Phase transition #Physics #Physics of Superconductivity and Magnetism #Quantum #Quantum Monte Carlo #Quantum many-body systems #Quantum mechanics #Scaling #Square lattice #Statistical physics #Theoretical and Computational Physics #cond-mat.stat-mech

paper · pdf · doi:10.1103/physrevb.78.064402

published as Phys. Rev. B 78, 064402 (2008) · 8 pages, 7 figures, differs slightly from published version

openalex publication_date 2008/08/05 · arxiv created 2008/09/05 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05

Abstract

A comprehensive study of the two-dimensional (2D) compass model on the square lattice is performed for classical and quantum spin degrees of freedom using Monte Carlo and quantum Monte Carlo methods. We employ state-of-the-art implementations using Metropolis, stochastic series expansion, and parallel tempering techniques to obtain the critical ordering temperatures and critical exponents. In a preinvestigation we reconsider the classical compass model where we study and contrast the finite-size scaling behavior of ordinary periodic boundary conditions against annealed boundary conditions. It is shown that periodic boundary conditions suffer from extreme finite-size effects which might be caused by closed-loop excitations on the torus. These excitations also appear to have severe effects on the Binder parameter. On this footing we report on a systematic Monte Carlo study of the quantum compass model. Our numerical results are at odds with recent literature on the subject which we trace back to neglecting the strong finite-size effects on periodic lattices. The critical temperatures are obtained as T_c=0.1464(2)J and T_c=0.055(1)J for the classical and quantum versions, respectively, and our data support a transition in the 2D Ising universality class for both cases.

Citations

• Quantum phase transition in the quantum compass model
• Critical Binder cumulant of two-dimensional Ising models
• Orbital ordering and frustrations
• Orbital Ordering in Charge Transfer Insulators
• Orbital order in classical models of transition-metal compounds
• Topologically Decoherence-Protected Qubits with Trapped Ions

Cited by

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

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