Critical behavior of the frustrated antiferromagnetic six-state clock model on a triangular lattice

Noh, Jiho; Rieger, Heiko; Enderle, M.; Knorr, K.

doi:10.1103/physreve.66.026111

Cited by 23 publications

(17 citation statements)

References 37 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…It is due to the fact that the moment ratio was used in Ref. [26], and the estimate of the KT temperature becomes higher because of large corrections to FSS [38].…”

Section: Kosterlitz-thouless Transitionsmentioning

confidence: 99%

“…It is quite interesting to investigate the effect of the q-fold symmetry-breaking fields in the case of the fully frustrated XY model. Quite recently, Noh et al [26] studied the AF six-state clock model on the triangular lattice using the Metropolis Monte Carlo simulation because of the experimental relevance to CF 3 Br monolayers physisorbed on graphite [27]. However, they did not pay attention to the lower temperature phase transition of KT type.…”

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Study of the fully frustrated clock model using the Wang–Landau algorithm

Surungan

Okabe

Tomita

2004

J. Phys. A: Math. Gen.

View full text Add to dashboard Cite

Monte Carlo simulations using the newly proposed Wang-Landau algorithm together with the broad histogram relation are performed to study the antiferromagnetic six-state clock model on the triangular lattice, which is fully frustrated. We confirm the existence of the magnetic ordering belonging to the Kosterlitz-Thouless (KT) type phase transition followed by the chiral ordering which occurs at slightly higher temperature. We also observe the lower temperature phase transition of KT type due to the discrete symmetry of the clock model. By using finite-size scaling analysis, the higher KT temperature T2 and the chiral critical temperature Tc are respectively estimated as T2 = 0.5154(8) and Tc = 0.5194(4). The results are in favor of the double transition scenario. The lower KT temperature is estimated as T1 = 0.496(2). Two decay exponents of KT transitions corresponding to higher and lower temperatures are respectively estimated as η2 = 0.25(1) and η1 = 0.13(1), which suggests that the exponents associated with the KT transitions are universal even for the frustrated model.

show abstract

“…It is due to the fact that the moment ratio was used in Ref. [26], and the estimate of the KT temperature becomes higher because of large corrections to FSS [38].…”

Section: Kosterlitz-thouless Transitionsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Study of the fully frustrated clock model using the Wang–Landau algorithm

Surungan

Okabe

Tomita

2004

J. Phys. A: Math. Gen.

View full text Add to dashboard Cite

show abstract

“…With added next-nearest-neighbor (NNN) FM interaction, both the three-state AFM Potts model 42 and the TAFI model [43][44][45][46] are known to have BKT-type phase transitions in the same universality class as the six-state clock model [47][48][49] . Under simple transformation the sixstate clock model is mapped to the TAFI model 46 .…”

Section: Introductionmentioning

confidence: 99%

Phase transition properties of the Bell-Lavis model

2014

View full text Add to dashboard Cite

Using Monte Carlo calculations we analyze the order and the universality class of phase transitions into a low density (honeycomb) phase of a triangular antiferromagnetic three-state Bell-Lavis model. The results are obtained in a whole interval of chemical potential µ corresponding to the honeycomb phase. Our results demonstrate that the phase transitions might be attributed to the three-state Potts universality class for all µ values except for the edges of the honeycomb phase existence. At the honeycomb phase and the low density gas phase boundary the transitions become of the first order. At another, honeycomb-to-frustrated phase boundary, we observe the approach to the crossover from the three-state Potts to the Ising model universality class. We also obtain the Schottky anomaly in the specific heat close to this edge. We show that the intermediate planar phase, found in a very similar antiferromagnetic triangular Blume-Capel model, does not occur in the Bell-Lavis model.

show abstract

“…[12]). The most recent Monte Carlo simulations [13,14,15,12] now show evidences in favor of the Ising universality class. The disagreement with older simulations may be due to the fact that the exponents tend to the expected Ising values only for large lattice sizes [15,12].…”

Section: Introductionmentioning

confidence: 94%

Numerical investigation of the ageing of the fully frustratedXYmodel

Walter¹,

Chatelain²

2009

J. Stat. Mech.

View full text Add to dashboard Cite

We study the out-of-equilibrium dynamics of the fully-frustrated XY model. At equilibrium, this model undergoes two phase transitions at two very close temperatures: a Kosterlitz-Thouless topological transition and a secondorder phase transition between a paramagnetic phase and a low-temperature phase where the chiralities of the lattice plaquettes are anti-ferromagnetically ordered. We compute by Monte Carlo simulations two-time spin-spin and chirality-chirality autocorrelation and response functions. From the dynamics of the spin waves in the low temperature phase, we extract the temperature-dependent exponent η. We provide evidences for logarithmic corrections above the Kosterlitz-Thouless temperature and interpret them as a manifestation of free topological defects. Our estimates of the autocorrelation exponent and the fluctuation-dissipation ratio differ from the XY values, while η(T KT) lies at the boundary of the error bar. Indications for logarithmic corrections at the second-order critical temperature are presented. However, the coupling between angles and chiralities is still strong and explains why autocorrelation exponent and fluctuation-dissipation ratio are far from the Ising values and seems stable.

show abstract

Critical behavior of the frustrated antiferromagnetic six-state clock model on a triangular lattice

Cited by 23 publications

References 37 publications

Study of the fully frustrated clock model using the Wang–Landau algorithm

Study of the fully frustrated clock model using the Wang–Landau algorithm

Phase transition properties of the Bell-Lavis model

Numerical investigation of the ageing of the fully frustratedXYmodel

Contact Info

Product

Resources

About