The Berezinskii-Kosterlitz-Thouless (BKT) transition in magnetic systems is an intriguing phenomenon, and estimating the BKT transition temperature is a long-standing problem. In this work, we explore anisotropic classical Heisenberg XY and XXZ models with ferromagnetic exchange on a square lattice and antiferromagnetic exchange on a triangular lattice using an unsupervised machine learning approach called principal component analysis (PCA). The earlier PCA studies of the BKT transition temperature (TBKT) using the vorticities as input fail to give any conclusive results, whereas, in this work, we show that the proper analysis of the first principal component-temperature curve can estimateTBKTwhich is consistent with the existing literature. This analysis works well for the anisotropic classical Heisenberg with a ferromagnetic exchange on a square lattice and for frustrated antiferromagnetic exchange on a triangular lattice. The classical anisotropic Heisenberg antiferromagnetic model on the triangular lattice has two close transitions: theTBKTand Ising-like phase transition for chirality atTc, and it is difficult to separate these transition points. It is also noted that using the PCA method and manipulation of their first principal component not only makes the separation of transition points possible but also determines transition temperature.The Berezinskii-Kosterlitz-Thouless (BKT) transition in magnetic systems is an intriguing phenomenon, and estimating the BKT transition temperature is a long-standing problem. In this work, we explore anisotropic classical Heisenberg XY and XXZ models with ferromagnetic exchange on a square lattice and antiferromagnetic exchange on a triangular lattice using an unsupervised machine learning approach called principal component analysis (PCA). The earlier PCA studies of the BKT transition temperature (TBKT) using the vorticities as input fail to give any conclusive results, whereas, in this work, we show that the proper analysis of the first principal component-temperature curve can estimateTBKTwhich is consistent with the existing literature. This analysis works well for the anisotropic classical Heisenberg with a ferromagnetic exchange on a square lattice and for frustrated antiferromagnetic exchange on a triangular lattice. The classical anisotropic Heisenberg antiferromagnetic model on the triangular lattice has two close transitions: theTBKTand Ising-like phase transition for chirality atTc, and it is difficult to separate these transition points. It is also noted that using the PCA method and manipulation of their first principal component not only makes the separation of transition points possible but also determines transition temperature.

arXiv:2205.15151Journal of Physics Condensed MatterJun 28, 20245 citations

An intermediate spherical model of a ferromagnet

Wayne W. Barrett

Journal of Statistical PhysicsApr 1, 19770 citations

Two-dimensionalXXZmodel on a square lattice: A Monte Carlo simulation

Alessandro Cuccoli, V. Tognetti, Ruggero Vaia

Results of Monte Carlo simulations of the ferromagnetic classical XXZ model on a square lattice are reported for interactions of the out of plane spin components \ensuremath{\lambda} varying between 0 and 0.99. For all the value of \ensuremath{\lambda} the signature of a Berezinskii-Kosterlitz-Thouless (BKT) phase transition was observed, and the corresponding critical temperature was located both by BKT fits and finite-size scaling methods. Data for in-plane and out of plane susceptibility, correlation length, specific heat, and internal energy are given in a broad range of temperature and for lattice sizes ranging from 32\ifmmode\times\else\texttimes\fi{}32 to 256\ifmmode\times\else\texttimes\fi{}256.Results of Monte Carlo simulations of the ferromagnetic classical XXZ model on a square lattice are reported for interactions of the out of plane spin components \ensuremath{\lambda} varying between 0 and 0.99. For all the value of \ensuremath{\lambda} the signature of a Berezinskii-Kosterlitz-Thouless (BKT) phase transition was observed, and the corresponding critical temperature was located both by BKT fits and finite-size scaling methods. Data for in-plane and out of plane susceptibility, correlation length, specific heat, and internal energy are given in a broad range of temperature and for lattice sizes ranging from 32\ifmmode\times\else\texttimes\fi{}32 to 256\ifmmode\times\else\texttimes\fi{}256.

Physical review. B, Condensed matterOct 1, 199588 citations

Magnetization Plateaus in Antiferromagnetic-(Ferromagnetic)nPolymerizedS=1/2XXZ Chains

Wei Chen, Kazuo Hida, B. C. Sanctuary

The plateau-non-plateau transition in the antiferromagnetic-(ferromagnetic) $_{n}$ polymerized $S=1/2$ XXZ chains under the magnetic field is investigated. The universality class of this transition belongs to the Brezinskii-Kosterlitz-Thouless (BKT) type. The critical points are determined by level spectroscopy analysis of the numerical diagonalization data for $4 \leq p \leq 13$ where $p(\equiv n+1)$ is the size of a unit cell. It is found that the critical strength of ferromagnetic coupling decreases with $p$ for small $p$ but increases for larger enough $p$ . It is also found that the plateau for large $p$ is wide enough for moderate values of exchange coupling so that it should be easily observed experimentally. This is in contrast to the plateaus for $p = 3$ chains which are narrow for a wide range of exchange coupling even away from the critical point.The plateau-non-plateau transition in the antiferromagnetic-(ferromagnetic)$_{n}$ polymerized $S=1/2$ XXZ chains under the magnetic field is investigated. The universality class of this transition belongs to the Brezinskii-Kosterlitz-Thouless (BKT) type. The critical points are determined by level spectroscopy analysis of the numerical diagonalization data for $4 \leq p \leq 13$ where $p(\equiv n+1)$ is the size of a unit cell. It is found that the critical strength of ferromagnetic coupling decreases with $p$ for small $p$ but increases for larger enough $p$. It is also found that the plateau for large $p$ is wide enough for moderate values of exchange coupling so that it should be easily observed experimentally. This is in contrast to the plateaus for $p = 3$ chains which are narrow for a wide range of exchange coupling even away from the critical point.

arXiv:cond-mat/0005544Journal of the Physical Society of JapanOct 15, 20005 citations

A spherical model of ferromagnet with a uniaxial anisotropuc interaction

H. Okamoto

Physics Letters AAug 1, 19703 citations

The plateau-non-plateau transition in the antiferromagnetic-(ferromagnetic)

_{n}

polymerized

S=1/2

XXZ chains under the magnetic field is investigated. The universality class of this transition belongs to the Brezinskii-Kosterlitz-Thouless (BKT) type. The critical points are determined by level spectroscopy analysis of the numerical diagonalization data for

4 \leq p \leq 13

where

p(\equiv n+1)

is the size of a unit cell. It is found that the critical strength of ferromagnetic coupling decreases with

p

for small

p

but increases for larger enough

p

. It is also found that the plateau for large

p

is wide enough for moderate values of exchange coupling so that it should be easily observed experimentally. This is in contrast to the plateaus for

p = 3

chains which are narrow for a wide range of exchange coupling even away from the critical point.