Monte Carlo study of the critical properties of the three-dimensional 120 degrees model

Sandro Wenzel
Elsevier Science, Reg Sales Off, Customer Support Dept, 655 Ave Of The Americas, New York, Ny 10010 Usa, 2011
Article de conférence

We report on large scale finite-temperature Monte Carlo simulations of the prototypical classical 120 degrees or e(g) model for orbital ordering on the simple cubic lattice in three dimensions. Our study reveals a continuous phase transition to an orbitally ordered phase with unusual critical properties compared to standard magnetism. While the correlation length exponent nu approximate to 0.665 is close to the 3D XY value, the exponent eta approximate to 0.15 differs substantially from O(N) values. Our results are corroborated by simulation results from a discrete e(g)-clock model that we have defined.

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Sandro Wenzel
Elsevier Science, Reg Sales Off, Customer Support Dept, 655 Ave Of The Americas, New York, Ny 10010 Usa, 2011
Article de conférence

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https://infoscience.epfl.ch/record/178571?ln=fr

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Monte Carlo study of the critical properties of the three-dimensional 120 degrees model

Sandro Wenzel

We report on large scale finite-temperature Monte Carlo simulations of the classical 120 degrees or e(g) orbital-only model on the simple cubic lattice in three dimensions with a focus towards its critical properties. This model displays a continuous phase transition to an orbitally ordered phase. While the correlation length exponent nu approximate to 0.665 is close to the 3D XY value, the exponent eta approximate to 0.15 differs substantially from O(N) values. We also introduce a discrete variant of the e(g) model, called the e(g)-clock model, which is found to display the same set of exponents. Further, an emergent U( 1) symmetry is found at the critical point T-c, which persists for T < T-c below a crossover length scaling as Lambda similar to xi(a), with an unusually small a approximate to 1.3.

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Unveiling the Nature of Three-Dimensional Orbital Ordering Transitions: The Case of e(g) and t(2g) Models on the Cubic Lattice

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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 approximate to 0.66(1) is close to the 3D XY value, the exponent eta approximate to 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 similar to xi(a), with an unusually small a approximate to 1.3. Finally, for the t(2g) model we find a first order transition into a low-temperature lattice-nematic phase without orbital order.

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