Phase transitions of the 6-clock model in two dimensions

Yamagata, Atsushi; Ono, Ikuo

doi:10.1088/0305-4470/24/1/033

Cited by 34 publications

(26 citation statements)

References 29 publications

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“…3. The estimate of T 2 is 0.9008(6), which is more precise than the previous estimates; 0.92(1) [11] and 0.90 [12]. The plot of m 2 (L) at T 2 (L) as a function of L for the 6-state clock model is given in Fig.…”

Section: Clock Modelmentioning

confidence: 63%

Probability-changing cluster algorithm for two-dimensionalXYand clock models

Tomita

Okabe

2002

Phys. Rev. B

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We extend the newly proposed probability-changing cluster (PCC) Monte Carlo algorithm to the study of systems with the vector order parameter. Wolff's idea of the embedded cluster formalism is used for assigning clusters. The Kosterlitz-Thouless (KT) transitions for the two-dimensional (2D) XY and q-state clock models are studied by using the PCC algorithm. Combined with the finite-size scaling analysis based on the KT form of the correlation length, ξ ∝ exp(c/ T /TKT − 1), we determine the KT transition temperature and the decay exponent η as TKT = 0.8933(6) and η = 0.243(5) for the 2D XY model. We investigate two transitions of the KT type for the 2D q-state clock models with q = 6, 8, 12, and for the first time confirm the prediction of η = 4/q 2 at T1, the low-temperature critical point between the ordered and XY-like phases, systematically.

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Section: Clock Modelmentioning

confidence: 63%

Probability-changing cluster algorithm for two-dimensionalXYand clock models

Tomita

Okabe

2002

Phys. Rev. B

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“…Based on the Mermin-Wagner theorem above mentioned, a discrete symmetry is important for the existence of a true LRO in 2D systems. It was theoretically predicted [10,11] and later confirmed numerically by several early studies [12,13,14] that the q-state clock models experience two transitions for q > 4, i.e., the lower (T 1 ) and the higher temperature (T 2 ) transitions, where the BKT phase exists between them. The typical characteristics of this phase is related to the existence of vortex-antivortex formation.…”

Section: Introductionmentioning

confidence: 77%

Berezinskii–Kosterlitz–Thouless transition on regular and Villain types of q-state clock models

Surungan

Masuda

Komura

et al. 2019

J. Phys. A: Math. Theor.

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We study q-state clock models of regular and Villain types with q = 5, 6 using cluster-spin updates and observed double transitions in each model. We calculate the correlation ratio and size-dependent correlation length as quantities for characterizing the existence of Berezinskii-Kosterlitz-Thouless (BKT) phase and its transitions by large-scale Monte Carlo simulations. We discuss the advantage of correlation ratio in comparison to other commonly used quantities in probing BKT transition. Using finite size scaling of BKT type transition, we estimate transition temperatures and corresponding exponents. The comparison between the results from both types revealed that the existing transitions belong to BKT universality.

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“…For the clock model with q ≥ 6, there is no solution for Eq. (12). However, we can define a bond entanglement entropy via the normalized bond entanglement spectra in the original and dual space, respectively,…”

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confidence: 99%

Phase Transition of the q -State Clock Model: Duality and Tensor Renormalization

Chen

Liao

Xie

et al. 2017

Chinese Phys. Lett.

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We investigate the critical behavior and the duality property of the ferromagnetic q-state clock model on the square lattice based on the tensor-network formalism. From the entanglement spectra of local tensors defined in the original and dual lattices, we obtain the exact self-dual points for the model with q ≤ 5 and approximate self-dual points for q ≥ 6. We calculate accurately the lower and upper critical temperatures for the six-state clock model from the fixed-point tensors determined using the higher-order tensor renormalization group method and compare with other numerical results.

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Phase transitions of the 6-clock model in two dimensions

Cited by 34 publications

References 29 publications

Probability-changing cluster algorithm for two-dimensionalXYand clock models

Probability-changing cluster algorithm for two-dimensionalXYand clock models

Berezinskii–Kosterlitz–Thouless transition on regular and Villain types of q-state clock models

Phase Transition of the q -State Clock Model: Duality and Tensor Renormalization

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