Study of the Berezinskii-Kosterlitz-Thouless transition: An unsupervised machine learning approach

Haldar, Sumit; Rahaman, Sk Saniur; Kumar, Manoranjan

doi:10.48550/arxiv.2205.15151

Cited by 1 publication

(2 citation statements)

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“…We prepare many vortex configurations of the XY model and the XY-like XXZ model with ∆ = 0.95 for several lattice sizes L × L (L = 16,32,48,64,80,96,112) as training data of the neural network, which are made from the spin configurations by calculating the vorticity on each plaquette. Here the spin configurations are generated by the Monte Carlo thermalization with 10 5 iterative steps based on the single-flip Metropolis algorithm.…”

Section: B Vortex Configurations Used As Training Datamentioning

confidence: 99%

“…Recently, several attempts have been made to detect the BKT transition in the XY model and the q-state clock model with machine learning techniques [24][25][26][27][28][29][30][31][32][33][34][35]. However, because the BKT transition is a phase transition without any spontaneous symmetry breakings, the machine learning techniques based basically on the pattern recognition are not necessarily powerful for its detection.…”

Section: Introductionmentioning

confidence: 99%

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Machine-learning detection of the Berezinskii-Kosterlitz-Thouless transition and the second-order phase transition in XXZ models

Miyajima

Mochizuki

2023

Phys. Rev. B

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We propose two machine-learning methods based on neural networks, which we respectively call the phase-classification method and the temperature-identification method, for detecting different types of phase transitions in the XXZ models without prior knowledge of their critical temperatures. The XXZ models have exchange couplings which are anisotropic in the spin space where the strength is represented by a parameter ∆(> 0). The models exhibit the second-order phase transition when ∆ > 1, whereas the Berezinskii-Kosterlitz-Thouless (BKT) phase transition when ∆ < 1. In the phase-classification method, the neural network is trained using spin or vortex configurations of wellknown classical spin models other than the XXZ models, e.g., the Ising models and the XY models, to classify those of the XXZ models to corresponding phases. We demonstrate that the trained neural network successfully detects the phase transitions for both ∆ > 1 and ∆ < 1, and the evaluated critical temperatures coincide well with those evaluated by conventional numerical calculations. In the temperature-identification method, on the other hand, the neural network is trained so as to identify temperatures at which the input spin or vortex configurations are generated by the Monte Carlo thermalization. The critical temperatures are evaluated by analyzing the optimized weight matrix, which coincide with the result of numerical calculation for the second-order phase transition in the Ising-like XXZ model with ∆ = 1.05 but cannot be determined uniquely for the BKT transition in the XY-like XXZ model with ∆ = 0.95.

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Section: B Vortex Configurations Used As Training Datamentioning

confidence: 99%