  Recently, generative machine-learning models have gained popularity in
physics, driven by the goal of improving the efficiency of Markov chain Monte
Carlo techniques and of exploring their potential in capturing experimental
data distributions. Motivated by their ability to generate images that look
realistic to the human eye, we here study generative adversarial networks
(GANs) as tools to learn the distribution of spin configurations and to
generate samples, conditioned on external tuning parameters, such as
temperature. We propose ways to efficiently represent the physical states,
e.g., by exploiting symmetries, and to minimize the correlations between
generated samples. We present a detailed evaluation of the various
modifications, using the two-dimensional XY model as an example, and find
considerable improvements in our proposed implicit generative model. It is also
shown that the model can reliably generate samples in the vicinity of the phase
transition, even when it has not been trained in the critical region. On top of
using the samples generated by the model to capture the phase transition via
evaluation of observables, we show how the model itself can be employed as an
unsupervised indicator of transitions, by constructing measures of the model's
susceptibility to changes in tuning parameters.
