Competing nematic interactions in a generalized<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mrow><mml:mi>X</mml:mi><mml:mi>Y</mml:mi></mml:mrow></mml:math>model in two and three dimensions

Canova, Gabriel Antônio; Levin, Yan; Arenzon, Jeferson J.

doi:10.1103/physreve.94.032140

Cited by 40 publications

(41 citation statements)

References 70 publications

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“…For q > 3, the results in Refs [61,62] suggest the existence of new phases at intermediate values of ∆ that do not appear for either ∆ = 0 or 1. Since the existence and/or nature of some of those transitions are still disputed, it would be interesting to see the outcome of the neural networks in those cases.…”

Section: Q=8mentioning

confidence: 95%

Machine learning of phase transitions in the percolation andXYmodels

2019

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In this paper, we apply machine learning methods to study phase transitions in certain statistical mechanical models on the two dimensional lattices, whose transitions involve non-local or topological properties, including site and bond percolations, the XY model and the generalized XY model. We find that using just one hidden layer in a fully-connected neural network, the percolation transition can be learned and the data collapse by using the average output layer gives correct estimate of the critical exponent ν. We also study the Berezinskii-Kosterlitz-Thouless transition, which involves binding and unbinding of topological defects-vortices and anti-vortices, in the classical XY model. The generalized XY model contains richer phases, such as the nematic phase, the paramagnetic and the quasi-long-range ferromagnetic phases, and we also apply machine learning method to it. We obtain a consistent phase diagram from the network trained with only data along the temperature axis at two particular parameter ∆ values, where ∆ is the relative weight of pure XY coupling. Besides using the spin configurations (either angles or spin components) as the input information in a convolutional neural network, we devise a feature engineering approach using the histograms of the spin orientations in order to train the network to learn the three phases in the generalized XY model and demonstrate that it indeed works. The trained network by using system size L × L can be used to the phase diagram for other sizes (L ′ × L ′ , where L ′ = L) without any further training.

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Section: Q=8mentioning

confidence: 95%

Machine learning of phase transitions in the percolation andXYmodels

2019

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“…Nevertheless, such investigations by MC simulations would require immense computational effort and it is out of the present scope. Furthermore, in the light of the recently found new phases in the model involving only two terms with q = 1 and q ≥ 5 [18,19], it would be interesting to explore the possibility of the existence of additional phases in the generalized XY model involving multiple terms with the q-values ranging between q min = 1 and q max ≥ 5.…”

Section: Summary and Discussionmentioning

confidence: 99%

“…Surprisingly, recent studies revealed that the model involving the q = 1 and q ≥ 5 terms displays a qualitatively different phase diagram featuring additional phases [18,19]. The latter appeared due to the competition between the respective couplings and the resulting phase transitions were determined to belong to different (Potts, Ising, or BKT) universality classes.…”

Section: Introductionmentioning

confidence: 99%

Multiple phase transitions in the XY model with nematic-like couplings

Žukovič

2018

Physics Letters A

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Critical behavior of the two-dimensional generalized XY model involving solely nematic-like terms of the second, third and fourth orders is studied by Monte Carlo method. We find that such a system can undergo three successive phase transitions. At higher temperatures there is a phase transition of the Berezinskii-Kosterlitz-Thouless type to the q = 4 nematic-like phase, followed by two more transitions of the Ising type to the q = 2 nematic-like and ferromagnetic phases, respectively. The q nematic-like phases are characterized by spin alignments with angles 2kπ/q, where k ≤ q is an integer. The ferromagnetic phase appears at low temperatures even without the presence of magnetic interactions owing to a synergic effect of the nematic-like terms.

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“…We can imagine this as an interaction between the spins considered as headless rods: spins which are parallel contribute less energy, even if they point in opposite directions. The T -∆ phase dia- gram of this model is explored in [47][48][49], and we see that at our chosen ∆ = 0.15, it undergoes two phase transitions as temperature increases. The first is an Ising-type transition from a magnetic phase to a nematic phase at T ≈ 0.3314 (as estimated using the magnetic susceptibility) resulting in (anti)vortices (which remain bound into vortex-antivortex pairs) stretching into domain walls with a half-(anti)vortex at each end; across the wall the spins flip by π.…”

Section: Nematic Xy Modelmentioning

confidence: 94%

Quantitative analysis of phase transitions in two-dimensional XY models using persistent homology

2022

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We use persistent homology and persistence images as an observable of three different variants of the two-dimensional XY model in order to identify and study their phase transitions. We examine models with the classical XY action, a topological lattice action, and an action with an additional nematic term. In particular, we introduce a new way of computing the persistent homology of lattice spin model configurations and, by considering the fluctuations in the output of logistic regression and k-nearest neighbours models trained on persistence images, we develop a methodology to extract estimates of the critical temperature and the critical exponent of the correlation length. We put particular emphasis on finite-size scaling behaviour and producing estimates with quantifiable error. For each model we successfully identify its phase transition(s) and are able to get an accurate determination of the critical temperatures and critical exponents of the correlation length.

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Competing nematic interactions in a generalizedXYmodel in two and three dimensions

Cited by 40 publications

References 70 publications

Machine learning of phase transitions in the percolation andXYmodels

Machine learning of phase transitions in the percolation andXYmodels

Multiple phase transitions in the XY model with nematic-like couplings

Quantitative analysis of phase transitions in two-dimensional XY models using persistent homology

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