Chiral exponents of the square-lattice frustrated<i>XY</i>model: A Monte Carlo transfer-matrix calculation

Granato, Enzo; Nightingale, M. P.

doi:10.1103/physrevb.48.7438

Cited by 72 publications

(78 citation statements)

References 25 publications

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“…The specific heat appeared to follow a power-law scaling rather than the logarithmic scaling as one would expect for the Ising universality class. A non-Ising scaling behavior is also observed in the studies of the FFXY model via a Monte Carlo simulation [6] and Monte Carlo transfer matrix calculations [7,8]. The same non-Ising critical behavior is also observed in the coupled XY -Ising model [5,9,10].…”

Section: Introductionsupporting

confidence: 62%

“…Frequently, it has been claimed [3][4][5][6][7][8] that the Ising-like transition and the KT-type transition occur at the same temperature. On the other hand, more recent studies have reported the transitions to occur at two different temperatures [11][12][13][14][15][16][17]19,20,22].…”

Section: Universality Classmentioning

confidence: 99%

“…Despite a lot of efforts [3][4][5][6][7][8][9][10][11][12][13][14][15][16][17][18][19][20][21][22], there is no consensus on the nature of the phase transitions and it is not clear whether the two transitions happen at two different temperatures or at a single one. Renormalization group (RG) studies on the FFXY model drew the conclusion that the transitions occur at the same temperature [3].…”

Section: Introductionmentioning

confidence: 99%

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

et al. 2002

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We study the anti-ferromagnetic six-state clock model with nearest neighbor interactions on a triangular lattice with extensive Monte-Carlo simulations. We find clear indications of two phase transitions at two different temperatures: Below TI a chirality order sets in and by a thorough finite size scaling analysis of the specific heat and the chirality correlation length we show that this transition is in the Ising universality class (with a non-vanishing chirality order parameter below TI ). At TKT (< TI ) the spin-spin correlation length as well as the spin susceptibility diverges according to a Kosterlitz-Thouless (KT) form and spin correlations decay algebraically below TKT . We compare our results to recent x-ray diffraction experiments on the orientational ordering of CF3Br monolayers physisorbed on graphite. We argue that the six-state clock model describes the universal feature of the phase transition in the experimental system and that the orientational ordering belongs to the KT universality class.

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Section: Introductionsupporting

confidence: 62%

Section: Universality Classmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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

et al. 2002

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“…12,18 In studies of the FFXY model, most authors find that there is a single transition with exponents deviating from Ising. 11,13,15,16 The hypothesis of the two transitions to be simultaneous is not always confirmed 14 or is rejected. 17 It is thus believed that the FFXY model is located in the phase diagram of the coupled XY -Ising model close to the merging of the Ising and KT lines.…”

Section: Discussionmentioning

confidence: 99%

“…[11][12][13][14][15][16][17] The generic version of this type of models, the coupled XY -Ising model, 12,18 is actually dual to the clock step model of Den Nijs 5 in the zero chirality limit. In the FFXY models, both transitions are found to be either closely separated 17 or simultaneous, and exponents deviating from Ising are found by many authors.…”

Section: Introductionmentioning

confidence: 99%

Roughening and preroughening in the six-vertex model with an extended range of interaction

Bastiaansen

Knops

1996

Phys. Rev. B

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We study the phase diagram of the body-centered solid on solid ͑BCSOS͒ model with an extended interaction range using transfer matrix techniques, pertaining to the ͑100͒ surface of single-component fcc and bcc crystals. The model shows a 2ϫ2 reconstructed phase and a disordered flat phase. The deconstruction transition between these phases merges with a Kosterlitz-Thouless line, showing an interplay of Ising and Gaussian degrees of freedom. As in studies of the fully frustrated XY model, exponents deviating from Ising are found. We conjecture that tricritical Ising behavior may be a possible explanation for the non-Ising exponents found in those models.

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Optimized Trial Functions Applied to Static and Dynamic Equilibrium Critical Phenomena, and Quantum Mechanical van der Waals Clusters

Nightingale

1997

Springer Proceedings in Physics

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Chiral exponents of the square-lattice frustratedXYmodel: A Monte Carlo transfer-matrix calculation

Cited by 72 publications

References 25 publications

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

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

Roughening and preroughening in the six-vertex model with an extended range of interaction

Optimized Trial Functions Applied to Static and Dynamic Equilibrium Critical Phenomena, and Quantum Mechanical van der Waals Clusters

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