The event-chain Monte Carlo (ECMC) algorithm is rejection-free and irreversible for Markov chain Monte Carlo simulations. Previous studies have revealed that the ECMC dynamics reduces the dynamical exponent z. In this study, we performed dynamical scaling analysis on systems simulated by the ECMC algorithm and estimated the exponent z for several systems. We show three things as follows. 1. For each model, an appropriate dynamical order parameter is proposed given that it is rotation-invariant, and its applicability to the ECMC dynamics is verified for nonequilibrium relaxation analysis. 2. These values of z are smaller than those obtained using Metropolis dynamics, which confirms that the ECMC dynamics is faster. 3. Although z in the three-dimensional ferromagnetic Heisenberg model is much less than $z \simeq 2$ , it is higher than $z \simeq 1$ reported in a previous work [Y. Nishikawa et al., Phys. Rev. E 92, 063306 (2015)].The event-chain Monte Carlo (ECMC) algorithm is rejection-free and irreversible for Markov chain Monte Carlo simulations. Previous studies have revealed that the ECMC dynamics reduces the dynamical exponent z. In this study, we performed dynamical scaling analysis on systems simulated by the ECMC algorithm and estimated the exponent z for several systems. We show three things as follows. 1. For each model, an appropriate dynamical order parameter is proposed given that it is rotation-invariant, and its applicability to the ECMC dynamics is verified for nonequilibrium relaxation analysis. 2. These values of z are smaller than those obtained using Metropolis dynamics, which confirms that the ECMC dynamics is faster. 3. Although z in the three-dimensional ferromagnetic Heisenberg model is much less than $z \simeq 2$, it is higher than $z \simeq 1$ reported in a previous work [Y. Nishikawa et al., Phys. Rev. E 92, 063306 (2015)].

Journal of the Physical Society of JapanJul 21, 20231 citation

Monte Carlo simulation of model spin systems

S. Ramasesha

Proceedings of the Indian Academy of Sciences Section C Engineering SciencesMar 1, 19791 citation

Dynamical Criticality of a Machine-learning-assisted Monte Carlo algorithm for a Mean-Field Spin Glass model

Seiya Miyamoto, Masayuki Ohzeki, Yoshihiko Nishikawa

We critically assess the performance of an autoregressive generative neural network model by applying it to an antiferromagnetic Ising model on a random regular graph. We train the network on equilibrium configurations in the low-temperature spin-glass phase of the model and perform Monte Carlo simulations using spin configurations generated by the network. The relaxation time of the Monte Carlo simulations drastically decreases with increasing the size of the training dataset and converges to an optimal value. The dynamical exponent characterizing the growth of the optimal relaxation time as a function of the system size is slightly reduced compared to the local Monte Carlo dynamics. However, we find that the size of the training dataset to achieve the optimal performance grows much faster with the system size than the relaxation time, implying that the total training cost eventually hinders a practical use of the method at large system sizes.We critically assess the performance of an autoregressive generative neural network model by applying it to an antiferromagnetic Ising model on a random regular graph. We train the network on equilibrium configurations in the low-temperature spin-glass phase of the model and perform Monte Carlo simulations using spin configurations generated by the network. The relaxation time of the Monte Carlo simulations drastically decreases with increasing the size of the training dataset and converges to an optimal value. The dynamical exponent characterizing the growth of the optimal relaxation time as a function of the system size is slightly reduced compared to the local Monte Carlo dynamics. However, we find that the size of the training dataset to achieve the optimal performance grows much faster with the system size than the relaxation time, implying that the total training cost eventually hinders a practical use of the method at large system sizes.

arXiv:2607.20243Jul 22, 20260 citations

Monte Carlo studies of critical phenomena in spin lattice systems

Akai Kurbanovich Murtazaev

Uspekhi Fizicheskih NaukJan 1, 20069 citations

z \simeq 2

, it is higher than

z \simeq 1

reported in a previous work [Y. Nishikawa et al., Phys. Rev. E 92, 063306 (2015)].