Two Types of Ordering in the Three-State Antiferromagnetic Potts Model on 3D Lattices: Monte Carlo Evidence

Lapinskas, S.; Rosengren, Anders

doi:10.1103/physrevlett.81.1302

Cited by 7 publications

(13 citation statements)

References 16 publications

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“…A few previous theories predicted the presence of multiple phase transitions in a model related to ours, [23][24][25][26][27][28][29][30][31][32] but our result is not consistent with their prediction. The system size dependence of this peak is shown in the inset of Fig.…”

Section: Thermodynamicscontrasting

confidence: 99%

“…As explained before, the antiferro 3-state Potts model is a much simpler model that has the same symmetry with our models; each microscopic pseudospin can point to only three directions, which corresponds to the limit of c → ∞ in the model (7). Although there have been a pile of studies about this problem for the Potts case on bipartite lattices, [23][24][25][26][27][28][29][30][31] several important points are not settled down about this model. Most importantly, the nature of the ordered states has not been well clarified for the Potts case.…”

Section: Low-temperature Ordered Phasementioning

confidence: 99%

“…Most importantly, the nature of the ordered states has not been well clarified for the Potts case. [23][24][25][26][27][28][29][30][31][32] The consensus is that the lowest-temperature phase is the broken sublattice-symmetry (BSS) state. 23) This is the phase in which the symmetry between the two sublattices is broken and this may also be called a ferri state.…”

Section: Low-temperature Ordered Phasementioning

confidence: 99%

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Classical Monte Carlo Study for Antiferro Quadrupole Orders in a Diamond Lattice

Hattori

Tsunetsugu

2016

J. Phys. Soc. Jpn.

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We investigate antiferro quadrupole orders in a diamond lattice under magnetic fields by Monte Carlo simulations for two types of classical effective models. One is an XY model with Z3 anisotropy, and the other is a two-component φ 4 model with a third-order anisotropy. We confirm that the universality class of the zero-field transition is that for the three-dimensional XY model. Magnetic field corresponds to a Z3 field in the effective model, and under this field, we find that collinear and canted antiferro-quadrupole orders compete. Each phase is characterized by symmetry breaking in the sector of (sublattice Z2)⊗(reflection Z2 for the order parameter). When Z3 anisotropy and magnetic field vary, it turns out that this system is a good playground for various multicritical points; bicritical and tetracritical points emerge in a finite field. Another important finding is about the scaling of parasitic ferro quadrupole order at the zero-field critical point. This is the secondary order parameter induced by the primary antiferro order, and its critical exponent β ′ =0.815 clearly differs from the expected value that is twice the value for the primary order parameter. The corresponding correlation length exponent is also different, ν ′ =0.597(12). We also discuss relation of the present effective quadrupole models with the 3-state Potts model as well as implication to undertanding of orbital orders in Pr-based 1-2-20 compounds.

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Section: Thermodynamicscontrasting

confidence: 99%

Section: Low-temperature Ordered Phasementioning

confidence: 99%

Section: Low-temperature Ordered Phasementioning

confidence: 99%

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Classical Monte Carlo Study for Antiferro Quadrupole Orders in a Diamond Lattice

Hattori

Tsunetsugu

2016

J. Phys. Soc. Jpn.

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“…The existing numerical data indicates that there is no such phase transition in the standard AFP model on the simple cubic lattice or in the standard 6CL model. However, such a transition may be possible in some modified models 21,22 . In fact, Blankschtein et al 3…”

Section: Conclusion and Discussionmentioning

confidence: 99%

Ordered phase and scaling inZnmodels and the three-state antiferromagnetic Potts model in three dimensions

Oshikawa

2000

Phys. Rev. B

120

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Based on a Renormalization-Group picture of Zn symmetric models in three dimensions, we derive a scaling law for the Zn order parameter in the ordered phase. An existing Monte Carlo calculation on the three-state antiferromagnetic Potts model, which has the effective Z6 symmetry, is shown to be consistent with the proposed scaling law. It strongly supports the Renormalization-Group picture that there is a single massive ordered phase, although an apparently rotationally symmetric region in the intermediate temperature was observed numerically.75.10.Hk, 05.50+q

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“…One of the phases of the antiferromagnetic Potts model on a bipartite lattice has a broken sublattice symmetry ͑BSS͒: one sublattice is dominated by one color, while the other is randomly populated by the two remaining colors. 24,25 With this state in mind, we have measured the average bond variables in the intermediate phase in the Monte Carlo simulations.…”

Section: B Bond Ordermentioning

confidence: 99%

Partial order from disorder in a classical pyrochlore antiferromagnet

2008

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We investigate theoretically the phase diagram of a classical Heisenberg antiferromagnet on the pyrochlore lattice perturbed by a weak second-neighbor interaction J_2. The huge ground state degeneracy of the nearest-neighbor Heisenberg spins is lifted by J_2 and a magnetically ordered ground state sets in upon approaching zero temperature. We have found a new, partially ordered phase with collinear spins at finite temperatures for a ferromagnetic J_2. In addition to a large nematic order parameter, this intermediate phase also exhibits a layered structure and a bond order that breaks the sublattice symmetry. Thermodynamic phase boundaries separating it from the fully disordered and magnetically ordered states scale as 1.87 J_2 S^2 and 0.26 J_2 S^2 in the limit of small J_2. The phase transitions are discontinuous. We analytically examine the local stability of the collinear state and obtain a boundary T ~ J_2^2/J_1 in agreement with Monte Carlo simulations.Comment: 14 pages revtex, revised phase diagram, references adde

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Two Types of Ordering in the Three-State Antiferromagnetic Potts Model on 3D Lattices: Monte Carlo Evidence

Cited by 7 publications

References 16 publications

Classical Monte Carlo Study for Antiferro Quadrupole Orders in a Diamond Lattice

Classical Monte Carlo Study for Antiferro Quadrupole Orders in a Diamond Lattice

Ordered phase and scaling inZnmodels and the three-state antiferromagnetic Potts model in three dimensions

Partial order from disorder in a classical pyrochlore antiferromagnet

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