Berezinskii--Kosterlitz--Thouless transition of the two-dimensional XY model on the honeycomb lattice

2024/06/21 by Jiang, Fu-Jiun
#FOS: Physical sciences #High Energy Physics - Lattice (hep-lat) #Statistical Mechanics (cond-mat.stat-mech)

paper · doi:10.48550/arxiv.2406.14812

Abstract

The Berezinskii--Kosterlitz--Thouless (BKT) transition of the two-dimensional XY model on the honeycomb lattice is investigated using both the techniques of Neural Network (NN) and Monte Carlo simulations. It is demonstrated in the literature that with certain plausible assumptions, the associated critical temperature T_BKT,H is found to be (1)/(√(2)) exactly. Surprisingly, the value of T_BKT,H obtained from our NN calculations is 0.560(9) which deviates significantly from (1)/(√(2)). In addition, based on the helicity modulus, the T_BKT,H determined is 0.571(8) agreeing well with that resulting from the NN estimation. The outcomes presented in this study indicate that a detailed analytic calculation is desirable to solve the found discrepancy.

Related

• Berezinskii-Kosterlitz-Thouless transition in the XY model on the honeycomb lattice: A comprehensive Monte Carlo analysis
• Berezinskii--Kosterlitz--Thouless transition -- a universal neural network study with benchmarking
• Bijecting the BKT transition
• First-order and Berezinskii-Kosterlitz-Thouless phase transitions in two-dimensional generalized XY models
• Study of the Berezinskii-Kosterlitz-Thouless transition: An unsupervised machine learning approach