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arXiv:2203.04012

Machine learning of Ising criticality with spin-shuffling

Pallab Basu, Jyotirmoy Bhattacharya, Dileep Pavan Surya Jakka, Chuene Mosomane, Vishwanath Shukla

Published Mar 8, 2022• 1 citation
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Abstract

We investigate the performance of neural networks in identifying critical behaviour in the 2D Ising model with next-to-nearest neighbour interactions. We train DNN and CNN based classifiers on the Ising model configurations with nearest neighbour interactions and test the ability of our models to identify the critical (cross-over) region, as well as the phases in the presence of next-to-nearest neighbour interactions. Our main objective is to investigate whether our models can learn the notion of criticality and universality, in contrast to merely identifying the phases by simply learning the value of the order parameter, magnetization in this case. We design a simple adversarial training process which forces our models to ignore learning about the order parameter while training. We find that such models are able to identify critical region with reasonable success, implying that it has learned to identify the structure of spin-spin correlations near criticality.

DOI
10.48550/arxiv.2203.04012

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We study the phase transitions of the two-dimensional antiferromagnetic Ising model with nearest J1J_1J1​ and next-to-nearest J2J_2J2​ interactions on the triangular lattice for J2/J1=0.1,0.5J_2/J_1 = 0.1, 0.5J2​/J1​=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 J2/J1J_2/J_1J2​/J1​ 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 J2/J1=0.1,0.5J_2/J_1 = 0.1, 0.5J2​/J1​=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.
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Abstract Phase transitions play a central role in statistical physics and are well understood in systems at thermal equilibrium. However, their nonequilibrium counterparts remain less explored because of the lack of a unified theoretical framework. In this study, we examine the potential of deep learning, specially convolutional neural networks (CNN), to detect nonequilibrium phase transitions (NEPT) in a 2D Ising model-like square lattice ferromagnetic system under effective parameter h . Without this parameter ( h = 0 ), we generate equilibrium spin configurations using the standard Metropolis algorithm as usual. With h ≠ 0 , we generate nonequilibrium spin configurations using an effective Glauber update rule which breaks detailed balance. While the former is used to train CNN, the later is not subsequently described by the usual Boltzmann-Gibbs distribution rather used to test the model. The study shows that the trained CNN can distinguish between ordered and disordered nonequilibrium steady states and accurately predict the critical temperature of the system undergoing NEPT. Finite size scaling analysis of the model’s output (perdition) reproduces critical exponents that agree with theoretical expectations, indicating that this method provides a strong, data driven approach for examining nonequilibrium critical phenomena.