  In lattice field theory, Monte Carlo simulation algorithms get highly
affected by critical slowing down in the critical region, where autocorrelation
time increases rapidly. Hence the cost of generation of lattice configurations
near the critical region increases sharply. In this paper, we use a Conditional
Generative Adversarial Network (C-GAN) for sampling lattice configurations. We
train the C-GAN on the dataset consisting of Hybrid Monte Carlo (HMC) samples
in regions away from the critical region, i.e., in the regions where the HMC
simulation cost is not so high. Then we use the trained C-GAN model to generate
independent samples in the critical region. Thus, the overall computational
cost is reduced. We test our approach for Gross-Neveu model in 1+1 dimension.
We find that the observable distributions obtained from the proposed C-GAN
model match with those obtained from HMC simulations, while circumventing the
problem of critical slowing down.
