Antiferromagnetic Triangular Ising Model with Ferromagnetic Next Nearest Neighbor Interactions –Transfer Matrix Method–

Kitatani, Hidetsugu; Oguchi, Takehiko

doi:10.1143/jpsj.57.1344

Cited by 17 publications

(30 citation statements)

References 11 publications

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“…Next, we move on to the anisotropic case K 2 = 0. As asserted by KO, there is a plausible reason to expect that anisotropic NNN F coupling plays the same role as the isotropic one [14], i.e., it only reduces the Gaussian coupling down to a certain value [7]. However, there is no reason to expect that ζ = 2/ √ 3 is appropriate to obtain a rotationally invariant description of the model in the 2D Euclidean space.…”

Section: A Effective Field Theory In the Sine-gordon Languagementioning

confidence: 99%

“…Although x 0 (l) and x 1 (l) [x s (l) and x 4 (l)] largely deviate from the free-boson value 2 ( 1 2 ) due to the logarithmic corrections, their main parts cancel each other in Eqs. (14) and (15). Therefore, the average x av (x ′ av ), the left-hand side of Eq.…”

Section: B Effective Geometric Factor Central Charge and Consistenmentioning

confidence: 99%

“…Therefore, the average x av (x ′ av ), the left-hand side of Eq. (14) [Eq. (15)], takes the value close to 2 ( 1 2 ).…”

Section: B Effective Geometric Factor Central Charge and Consistenunclassified

“…Thus, two types of Berezinskii-Kosterlitz-Thouless (BKT) transition lines are expected to separate the critical region from the ordered and disordered phases [18,19]. Actually, Kitatani and Oguchi (KO) performed the transfermatrix (TM) calculations at the ratio K 2 /K 1 = 0.5 in order to evaluate the β function within the Roomany-Wyld approximation [20] and the spin-spin correlation function, and then concluded the existence of the critical finite temperature region [14]. Subsequently, Miyashita, Kitatani, and Kanada performed large scale Monte Carlo (MC) simulation calculations and found the consistent results [21].…”

Section: Introductionmentioning

confidence: 99%

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Global phase diagram and six-state clock universality behavior in the triangular antiferromagnetic Ising model with anisotropic next-nearest-neighbor coupling: Level-spectroscopy approach

2006

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We investigate the triangular-lattice antiferromagnetic Ising model with a spatially anisotropic next-nearest-neighbor ferromagnetic coupling, which was first discussed by Kitatani and Oguchi. By employing the effective geometric factor, we analyze the scaling dimensions of the operators around the Berezinskii-Kosterlitz-Thouless (BKT) transition lines, and determine the global phase diagram. Our numerical data exhibit that two types of BKT-transition lines separate the intermediate critical region from the ordered and disordered phases, and they do not merge into a single curve in the antiferromagnetic region. We also estimate the central charge and perform some consistency checks among scaling dimensions in order to provide the evidence of the six-state clock universality. Further, we provide an analysis of the shapes of boundaries based on the crossover argument.

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Section: A Effective Field Theory In the Sine-gordon Languagementioning

confidence: 99%

Section: B Effective Geometric Factor Central Charge and Consistenmentioning

confidence: 99%

“…Therefore, the average x av (x ′ av ), the left-hand side of Eq. (14) [Eq. (15)], takes the value close to 2 ( 1 2 ).…”

Section: B Effective Geometric Factor Central Charge and Consistenunclassified

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Global phase diagram and six-state clock universality behavior in the triangular antiferromagnetic Ising model with anisotropic next-nearest-neighbor coupling: Level-spectroscopy approach

2006

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“…A simplification has been used in the latter approach: K nnn was taken to be nonzero only for four out of the six next-nearest neighbors [8][9][10]. This leads to a substantial simplification of the transfer matrix calculations, but FIG.…”

Section: Introductionmentioning

confidence: 99%

Triangular Ising model with nearest- and next-nearest-neighbor couplings in a field

Qian

Blöte

2004

Phys. Rev. E

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The authors study the Ising model on the triangular lattice with nearest-neighbor couplings K nn , nextnearest-neighbor couplings K nnn Ͼ 0, and a magnetic field H. This work is done by means of finite-size scaling of numerical results of transfer matrix calculations, and Monte Carlo simulations. We determine the phase diagram and confirm the character of the critical manifolds. The emphasis of this work is on the antiferromagnetic case K nn Ͻ 0, but we also explore the ferromagnetic regime K nn ജ 0 for H = 0. For K nn Ͻ 0 and H =0 we locate a critical phase presumably covering the whole range −ϱϽK nn Ͻ 0. For K nn Ͻ 0, H 0 we locate a plane of phase transitions containing a line of tricritical three-state Potts transitions. In the limit H → ϱ this line leads to a tricritical model of hard hexagons with an attractive next-nearest-neighbor potential.

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Coherent-Anomaly Method in Cooperative Phenomena: Some Applications to Polymer Physics

Hu¹,

Suzuki²

1989

Space-Time Organization in Macromolecular Fluids

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Antiferromagnetic Triangular Ising Model with Ferromagnetic Next Nearest Neighbor Interactions –Transfer Matrix Method–

Cited by 17 publications

References 11 publications

Global phase diagram and six-state clock universality behavior in the triangular antiferromagnetic Ising model with anisotropic next-nearest-neighbor coupling: Level-spectroscopy approach

Global phase diagram and six-state clock universality behavior in the triangular antiferromagnetic Ising model with anisotropic next-nearest-neighbor coupling: Level-spectroscopy approach

Triangular Ising model with nearest- and next-nearest-neighbor couplings in a field

Coherent-Anomaly Method in Cooperative Phenomena: Some Applications to Polymer Physics

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