Unveiling the nature of three dimensional orbital ordering transitions: the case of $e_g$ and $t_{2g}$ models on the cubic lattice

Abstract

We perform large scale finite-temperature Monte Carlo simulations of the classical $e_g$ and $t_{2g}$ orbital models on the simple cubic lattice in three dimensions. The $e_g$ model displays a continuous phase transition to an orbitally ordered phase. While the correlation length exponent $\nu \approx 0.66(1)$ is close to the 3D XY value, the exponent $\eta \approx 0.15(1)$ differs substantially from O(N) values. At $T_c$ a U(1) symmetry emerges, which persists for $T<T_c$ below a crossover length scaling as $\Lambda \sim {\xi }^a$, with an unusually small $a\approx 1.3$. Finally, for the $t_{2g}$ model we find a {\em first order} transition into a low-temperature lattice-nematic phase without orbital order.

arXiv comment4 pages, 5 figures

References in corpus (22)

• Anyons in an exactly solved model and beyond
• Mott Insulators in the Strong Spin-Orbit Coupling Limit: From Heisenberg to a Quantum Compass and Kitaev Models
• Critical Phenomena and Renormalization-Group Theory
• Controlling Spin Exchange Interactions of Ultracold Atoms in Optical Lattices
• A toolbox for lattice spin models with polar molecules
• Kitaev-Heisenberg Model on Honeycomb Lattice: Possible Exotic Phases in Iridium Oxides $A_2$IrO${}_3$
• Critical behavior of the three-dimensional XY universality class
• Superconducting Nanocircuits for Topologically Protected Qubits
• Protected Qubits and Chern Simons theories in Josephson Junction Arrays
• Discrete Sliding Symmetries, Dualities, and Self-dualities of Quantum Orbital Compass Models and (p+ip) Superconducting Arrays
• Orbital order in classical models of transition-metal compounds
• Emergence of U(1) symmetry in the 3D XY model with Zq anisotropy
• Directional Ordering of Fluctuations in a Two-dimensional Compass Model
• Ordered phase and scaling in $Z_n$ models and the three-state antiferromagnetic Potts model in three dimensions
• Monte Carlo simulations of the directional-ordering transition in the two-dimensional classical and quantum compass model
• Unconventional continuous phase transition in a three dimensional dimer model
• Phase diagram of an extended classical dimer model
• Orbital ordering in transition-metal compounds: I. The 120-degree model
• Orbital ordering in e_g orbital systems: Ground states and thermodynamics of the 120 degree model
• Re-examining the directional-ordering transition in the compass model with screw-periodic boundary conditions
• Randomly Diluted e_g Orbital-Ordered Systems
• The Quantum Compass Model on the Square and Simple Cubic Lattices

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