arXiv subjects

Fu-Jiun Jiang

Publications and source records attributed to Fu-Jiun Jiang.

At least 19 recordsLinked to original sources

arXiv2025

A Machine Learning study of the two-dimensional antiferromagnetic $q$-state Potts model on the square lattice

The critical phenomena of two-dimensional (2D) antiferromagnetic $q$-state Potts model on the square lattice with $q=2,3,4,5$ and 6 are investigated using the technique of supervised neural network (NN). Unlike the conventional NN approaches, here we train a multilayer perceptron consisting of only one input layer, one hidden layer, and one output layer with two artificially made stagger-like configurations. Remarkably, despite the fact that the MLP is trained without any input from these considered models, it correctly identifies the critical temperatures of the studied physical systems. Particularly, the MLP outcomes suggest convincingly that the $q=3$ model is critical only at zero temperature and $q=4,5,6$ models remain disordered at all temperatures. Previously, this MLP has been successfully applied to uncover the nature of the phase transitions of 2D antiferromagnetic Ising model with multi-interactions. Therefore, it will be interesting to examine whether the already trained MLP can detect other models with untypical critical phenomena.

hep-lat↗

arXiv2025

A Machine Learning study of the two-dimensional antiferromagnetic Ising model with nearest and next-to-nearest interactions on the triangular lattice

We study the phase transitions of the two-dimensional antiferromagnetic Ising model with nearest $J_1$ and next-to-nearest $J_2$ interactions on the triangular lattice for $J_2/J_1 = 0.1, 0.5$ and 1.0. The method of supervised neural networks (NN) is employed for the investigation. While supervised NN is used, no real spin configurations are needed for the training. In addition, two kinds of configurations having their spins be arranged in a staggered pattern are considered as the training set. Remarkably, with this unconventional training strategy, not only the critical temperatures of the studied $J_2/J_1$ are computed accurately by the resulting NN, but also the nature of the investigated phase transitions are determined correctly. Specifically, the phase transitions associated with $J_2/J_1 = 0.1, 0.5$ and 1.0 are first order. These conclusions are consistent with the known results obtained by other methods. Since the training strategy is simple, the NN calculations is highly efficient. It remains to examine whether the unconventional training approach considered in this study can be used to investigate other models with untypical phase transitions or with nontrivial ground state configurations.

hep-lat↗

arXiv2025

The phase transitions of the frustrated $J_1$-$J_2$ Ising model on the honeycomb lattice

We study the phase transitions of the frustrated $J_1$-$J_2$ Ising model on the honeycomb lattice using the non-perturbative first principle Monte Carlo simulations. Here $J_1 < 0$ and $J_2 > 0$ are the nearest and next-to-nearest couplings, respectively. In particular, the values of $J_2/|J_1| = 0.20, 0.22, 0.23, 0.24, 0.3, 0.5, 0.8,$ and 1.0 are considered in our study. Based on the numerical outcomes, we find that the phase transitions for $J_2/|J_1| = 0.20, 0.22, 0.23,$ and 0.24 are second order and are governed by the 2D Ising universality class. In addition, we find evidence to support the facts that there are transitions for $J_2/|J_1| = 0.5, 0.8$ and 1.0 and these phase transitions are second order. Our results also indicate phase transition is unlikely to take place for $g=0.3$. We are not able to obtain results for $J_2/|J_1|$ $\in$ (0.24, 0.3) because the associated integrated autocorrelation times or (and) the equilibrium times are extremely large at the low-temperature region. A comparison between the outcomes presented here and the available results in the literature is briefly conducted as well.

hep-lat↗

arXiv2025

Comments on the minimal training set for CNN: a case study of the frustrated $J_1$-$J_2$ Ising model on the square lattice

The minimal training set to train a working CNN is explored in detail. The considered model is the frustrated $J_1$-$J_2$ Ising model on the square lattice. Here $J_1 < 0$ and $J_2 > 0$ are the nearest and next-to-nearest neighboring couplings, respectively. We train the CNN using the configurations of $g \stackrel{\text{def}}{=} J_2/|J_1| = 0.7$ and employ the resulting CNN to study the phase transition of $g = 0.8$. We find that this transfer learning is successful. In particular, only configurations of two temperatures, one is below and one is above the critical temperature $T_c$ of $g=0.7$, are needed to reach accurately determination of the $T_c$ of $g=0.8$. However, it may be subtle to use this strategy for the training. Specifically, for the considered model, due to the inefficiency of the single spin flip algorithm used in sampling the configurations at the low-temperature region, the two temperatures associated with the training set should not be too far away from the $T_c$ of $g=0.7$, otherwise, the performance of the obtained CNN is not of high quality, hence cannot determine the $T_c$ of $g=0.8$ accurately. For the considered model, we also uncover the condition for training a successful CNN when only configurations of two temperatures are considered as the training set.

hep-lat↗

arXiv2025

A Bond weighted tensor renormalization group study of the q-state ferromagnetic Potts models on the square lattice

It is known rigorously that the phase transition of the $q$-state ferromagnetic Potts model on the square lattice is second order for $q=4$. Despite this fact, some observables of the $q=4$ model show features of a first-order phase transition. For example, negative peak appears for the quantity of Binder ratio $Q_2$ of this model. Such a non-monotonic behavior of $Q_2$ is typically a consequence of phase coexistence, hence is served as a signal of a first-order phase transition. In particular, the negative peak should diverge with linear system size $L$ squared. Since the mentioned divergence phenomenon is not observed for the 4-state Potts model, the scenario of a first-order phase transition for this model is ruled out. Interestingly, a recent large scale Monte Carlo investigation of the 4-state Potts model observes that the two-peak structure of the energy density distribution becomes more noticeable when $L$ increases. This finding indicates the signal of coexistence of phases is getting stronger with $L$. Due to these unusual critical behaviors, here we study the energy density $E$ and the specific heat $C_v$ of the 4-state Potts model on the square lattice using the technique of bond weighted tensor renormalization group (BWTRG). For a comparison purpose, $q=2$ and $q=5$ ferromagnetic Potts models on the square lattice are investigated using the same method as well. Remarkably, our results do imply there may be a small energy gap for $q=4$ model. While the appearance of the mentioned small energy gap can be explained plausibly and it will disappear with a more sophisticated investigation, our finding suggests that whether a message of a first-order phase transition is genuine or is an artificial effect requires further and detailed investigations.

cond-mat.stat-mech↗

arXiv2025

A Monte Carlo examination for the numerical values of universal quantities in spatial dimension two

By simulating a two-dimensional (2D) dimerized spin-1/2 antiferromagnet with the quantum Monte Carlo method, the numerical values of two universal quantities associated with the quantum critical regime (QCR), namely $S(π,π)/\left(χ_s T\right)$ and $c/\left(Tξ\right)$, are determined. Here $S(π,π)$, $χ_s$, $c$, $ξ,$ and $T$ are the staggered structure factor, the staggered susceptibility, the spin-wave velocity, the correlation length, and the temperature, respectively. For other QCR universal quantities, such as the Wilson ratio $W$ and $χ_u c^2/T$ ($χ_u$ is the uniform susceptibility), it is shown that the addition of higher order theoretical contribution makes the agreement between the numerical and the analytic results worse. We find that the same scenario applies to $S(π,π)/\left(χ_s T\right)$ and $c/\left(Tξ\right)$ as well. Specifically, our calculations lead to $S(π,π)/\left(χ_s T\right)\sim 1.073$ and $c/\left(Tξ\right)\sim 0.963$ which are in better consistence with the leading theoretical predictions than those with the next-to-leading order terms. The presented outcome here as well as those in some relevant literature suggest that it is desirable to conduct a refinement of the analytic calculation to resolve the puzzle of why the inclusion of higher order terms leads to less accurate predictions for these universal quantities.

cond-mat.str-el↗

arXiv2024

A neural network study of the phase transitions of the two-dimensional antiferromagnetic $q$-state Potts models on the square lattice

The critical phenomena of the two-dimensional antiferromagnetic $q$-state Potts model on the square lattice with $q=2,3,4$ are investigated using the techniques of neural networks (NN). In particular, an unconventional supervised NN which is trained using no information about the physics of the considered systems is employed. In addition, conventional unsupervised autoencoders (AECs) are used in our study as well. Remarkably, while the conventional AECs fail to uncover the critical phenomena of the systems investigated here, our unconventional supervised NN correctly identifies the critical behaviors of all three considered antiferromagnetic $q$-state models. The results obtained in this study suggest convincingly that the applicability of our unconventional supervised NN is broader than one anticipates. In particular, when a new system is studied with our NN, it is likely that it is not necessary to conduct any training, and one only needs to examine whether an appropriate reduced representation of the original raw configurations exists, so that the same already trained NN can be employed to explore the related phase transition efficiently.

hep-lat↗

arXiv2024

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

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 $T_{\text{BKT,H}}$ is found to be $\frac{1}{\sqrt{2}}$ exactly. Surprisingly, the value of $T_{\text{BKT,H}}$ obtained from our NN calculations is 0.560(9) which deviates significantly from $\frac{1}{\sqrt{2}}$. In addition, based on the helicity modulus, the $T_{\text{BKT,H}}$ 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.

hep-lat↗

arXiv2023

Detection of Berezinskii--Kosterlitz--Thouless transitions for the two-dimensional $q$-state clock models with neural networks

Using the technique of supervised neural networks (NN), we study the phase transitions of two-dimensional (2D) 6- and 8-state clock models on the square lattice. The employed NN has only one input layer, one hidden layer of 2 neurons, and one output layer. In addition, the NN is trained without any prior information about the considered models. Interestingly, despite its simple architecture, the built supervised NN not only detects both the two Berezinskii--Kosterlitz--Thouless (BKT) transitions but also determines the transition temperatures with reasonable high accuracy. It is remarkable that a NN, which has an extremely simple structure and is trained without any input from the studied models, can be employed to study topological phase transitions. The outcomes shown here as well as those previously demonstrated in the literature suggest the feasibility of constructing a universal NN that is applicable to investigate the phase transitions of many systems.

cond-mat.dis-nn↗

arXiv2022

Machine learning phases of an Abelian gauge theory

The phase transition of the two-dimensional $U(1)$ quantum link model on the triangular lattice is investigated by employing a supervised neural network (NN) consisting of only one input layer, one hidden layer of two neurons, and one output layer. No information on the studied model is used when the NN training is conducted. Instead, two artificially made configurations are considered as the training set. Interestingly, the obtained NN not only estimates the critical point accurately but also uncovers the physics correctly. The results presented here imply that a supervised NN, which has a very simple architecture and is trained without any input from the investigated model, can identify the targeted phase structure with high precision.

hep-lat↗

arXiv2022

Unexpected results of the phase transitions of four-state Potts model on the square and the honeycomb lattices

It is widely believed that the phase transition for the four-state ferromagnetic Potts model on the square lattice is of the pseudo-first order. Specifically, it is expected that first-order phase transition behavior is found on small lattices and that the true nature of second-order phase transition only emerges with large system sizes. It is also intuitively expected that for other geometries, the types of the associated phase transitions should be identical to that of the square lattice. However, after simulating more than 16 million spins for the four-state Pott model, we observe that a feature of first-order phase transition persists on the square lattice. Additionally, a characteristic of second-order phase transition already appears on a small honeycomb lattice. Indications of a pseudo-first-order phase transition were not found in our investigation. This suggests that a thorough analytic calculation may be required to develop a better understanding of the presented results.

cond-mat.stat-mech↗

arXiv2022

The numerical value for a universal quantity of a two-dimensional dimerized quantum antiferromagnet

The numerical value of a universal quantity associated with the quantum critical regime, namely $χ_u c^2/T$, for a two-dimensional (2D) dimerized spin-1/2 antiferromagnet is calculated using the quantum Monte Carlo simulations (QMC). Here $χ_u$, $c$, and $T$ are the uniform susceptibility, the spin-wave velocity, and the temperature, respectively. By simulating large lattices at moderately low temperatures, we find $χ_u c^2/T \sim 0.32$. Our estimation of $χ_u c^2/T$ deviates from the related analytic prediction but agrees with recent numerical calculations of other 2D dimerized spin-1/2 antiferromagnets.

cond-mat.str-el↗

arXiv2021

Neural network evidence of a weakly first order phase transition for the two-dimensional 5-state Potts model

A universal (supervised) neural network (NN), which is only trained once on a one-dimensional lattice of 200 sites, is employed to study the phase transition of the two-dimensional (2D) 5-state ferromagnetic Potts model on the square lattice. In particular, the NN is obtained by using merely two artificially made configurations as the training set. Due to the elegant features of the considered NN, results associated with systems consisting of over 4000000 spins can be obtained with ease, and convincing evidence showing the investigated phase transition is weakly first order is reached. The outcomes demonstrated here can hardly be achieved with the standard NNs that are commonly used in the literature.

cond-mat.stat-mech↗

arXiv2020

Unpolarized Dihadron Fragmentation Functions in Nonlocal Chiral Quark Model

We have calculated the unpolarized dihadron fragmentation functions (uDiFFs) of pions and kaons using the nonlocal chiral-quark model (NLChQM) and evolved our results to the transferred momentum scale Q$^2$=4$\mathrm{GeV}^2$ by the QCD evolution equations. These uDiFFs have also been computed in the Nambu--Jona-Lasinio-jet (NJL-jet) model for the sake of comparison. We find that there is substantial difference between the results of these two models. Furthermore, the DiFFs of $u\to π^{+}π^{-}$ and $g\to π^{+}π^{-}$ at $Q^2=109\,\mathrm{GeV}^2$ in these two models are presented in comparison with the parametrizations fitted by the Monte Carlo event generator JETSET.

hep-ph↗

arXiv2019

Universal scaling of three-dimensional dimerized quantum antiferromagnets on bipartite lattices

Using the first principles quantum Monte Carlo (QMC) calculations, we investigate the previously established universal scaling between the Néel temperature $T_N$ and the staggered magnetization density $M_s$ of three-dimensional (3D) dimerized quantum antiferromagnets. Particularly, the calculations are done on both the stacked honeycomb and the cubic lattices. In addition to simulating models with two types of antiferromagnetic couplings (bonds) like those examined in earlier studies, here a tunable parameter controlling the strength of third type of bond is introduced. Interestingly, while the data of models with two types of bonds obtained here fall on top of the universal scaling curves determined previously, the effects due to microscopic details do appear. Moreover, the most striking result suggested in our study is that with the presence of three kinds of bonds in the investigated models, the considered scaling relations between $T_N$ and $M_s$ can be classified by the coordinate number of the underlying lattice geometries. The findings presented here broaden the applicability of the associated classification schemes formerly discovered. In particular, these results are not only interesting from a theoretical point of view, but also can serve as useful guidelines for the relevant experiments.

cond-mat.str-el↗

arXiv2017

Applications of neural networks to the studies of phase transitions of two-dimensional Potts models

We study the finite temperature (FT) phase transitions of two-dimensional (2D) $q$-states Potts models on the square lattice, using the first principles Monte Carlo (MC) simulations as well as the techniques of neural networks (NN). We demonstrate that the ideas from NN can be adopted to study these considered FT phase transitions efficiently. In particular, even with a simple NN constructed in this investigation, we are able to obtain the relevant information of the nature of these FT phase transitions, namely whether they are first order or second order. Our results strengthens the potential applicability of machine learning in studying various states of matters. Subtlety of applying NN techniques to investigate many-body systems is briefly discussed as well.

cond-mat.dis-nn↗

arXiv2017

Monte Carlo determination of the low-energy constants for a two-dimensional spin-1 Heisenberg model with spatial anisotropy

The low-energy constants, namely the spin stiffness $ρ_s$, the staggered magnetization density ${\cal M}_s$ per area, and the spinwave velocity $c$ of the two-dimensional (2D) spin-1 Heisenberg model on the square and rectangular lattices are determined using the first principles Monte Carlo method. In particular, the studied models have antiferromagnetic couplings $J_1$ and $J_2$ in the spatial 1- and 2-directions, respectively. For each considered $J_2/J_1$, the aspect ratio of the corresponding linear box sizes $L_2/L_1$ used in the simulations is adjusted so that the squares of the two spatial winding numbers take the same values. In addition, the relevant finite-volume and -temperature predictions from magnon chiral perturbation theory are employed in extracting the numerical values of these low-energy constants. Our results of $ρ_{s1}$ are in quantitative agreement with those obtained by the series expansion method over a broad range of $J_2/J_1$. This in turn provides convincing numerical evidence for the quantitative correctness of our approach. The ${\cal M}_s$ and $c$ presented here for the spatially anisotropic models are new and can be used as benchmarks for future related studies.

cond-mat.str-el↗

arXiv2015

Consistency check of charged hadron multiplicities and fragmentation functions in SIDIS

We derived the conditions on certain combinations of integrals of the fragmentation functions of pion using HERMES data of the sum for the charged pion multiplicities from semi-inclusive deep-inelastic scattering (SIDIS) off the deuteron target. In our derivation the nucleon parton distribution functions (PDFs) are assumed to be isospin SU(2) symmetric. Similar conditions have also been obtained for the fragmentation functions (FFs) of kaon by the sum of charged kaon multiplicities as well. We have chosen several FFs to study the impact of those conditions we have derived. Among those FFs, only that produced in the nonlocal chiral-quark model (NL$χ$QM) constantly satisfy the conditions. Furthermore, the ratios of the strange PDFs $S(x)$ and the nonstrange PDFs $Q(x,Q^2)$ extracted from the charged pion and kaon multiplicities differ from each other significantly. Finally, we demonstrate that the HERMES pion multiplicity data is unlikely to be compatible with the two widely-used PDFs, namely CTEQ6M and NNPDF3.0.

hep-ph↗