# Conditional generative models for sampling and phase transition indication in spin systems

### Submission summary

 As Contributors: Mathias Scheurer Preprint link: scipost_202103_00010v1 Date submitted: 2021-03-06 11:00 Submitted by: Scheurer, Mathias Submitted to: SciPost Physics Academic field: Physics Specialties: Artificial Intelligence Condensed Matter Physics - Computational Statistical and Soft Matter Physics Approaches: Theoretical, Computational

### Abstract

In this work, we study generative adversarial networks (GANs) as a tool to learn the distribution of spin configurations and to generate samples, conditioned on external tuning parameters or other quantities associated with individual configurations. For concreteness, we focus on two examples of conditional variables---the temperature of the system and the energy of the samples. We show that temperature-conditioned models can not only be used to generate samples across thermal phase transitions, but also be employed as unsupervised indicators of transitions. To this end, we introduce a GAN-fidelity measure that captures the model’s susceptibility to external changes of parameters. The proposed energy-conditioned models are integrated with Monte Carlo simulations to perform over-relaxation steps, which break the Markov chain and reduce auto-correlations. We propose ways of efficiently representing the physical states in our network architectures, e.g., by exploiting symmetries, and to minimize the correlations between generated samples. A detailed evaluation, using the two-dimensional XY model as an example, shows that these incorporations bring in considerable improvements over standard machine-learning approaches. We further study the performance of our architectures when no training data is provided near the critical region.

###### Current status:
Editor-in-charge assigned

### Submission & Refereeing History

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Submission scipost_202103_00010v1 on 6 March 2021

## Reports on this Submission

### Strengths

1. In the manuscript, authors first introduced the Generative Adversarial Networks (GANs) as a general tool to explore the topological phase transition emerges in continuous many-body systems.

2. The conditional GANs(c-GANS) show a good performance in generating samples unsupervisedly, which could reduce the auto-correlations on the Markov-Chain efficiently.

3. Two measures were proposed and first validated in detecting the BKT phase transition unsupervisedly.

### Weaknesses

1. The classical 2-D XY model shows the magnetization in the thermodynamic limit is zero, thus, it is not so convincing to show magnetization changes with the Temperature only for lattice size (16$\times$16 and 8$\times$8 ) in fig 2.

2. In ref.44, the authors proposed a sawtooth-type CNN filter to recognize the vortices hidden in configurations, but it still needs pre-training. One of my concerns is that, could we find a similar inner structure in GANs automatically? If not, besides the two measures inspired by thermodynamics, where is the feasibility of the GANs from?

3. From fig.2 to fig.5, the comparison between MCMC-samples and GANs (containing I-GAN-T and cGANs) reveals distinct mismatches. It needs more explanations from technical view or better from physical view.

### Report

In general, it is an exciting work which introduces the GANs into detecting topological phase transitions in many-body systems. The authors carefully investigated the applications of the GANs in both the efficiency of numerical computations and unsupervised detection of phase transitions.

Except the ref.70, at this time there is no similar work. And as emphasized by the authors in their manuscript, they adopted different technical and analytical frameworks compared with ref.70.

I recommend accepting this manuscript as an article in the journal.

• validity: high
• significance: high
• originality: top
• clarity: good
• formatting: excellent
• grammar: excellent