Explore the intricacies of perturbative expansion in energy densities within integrable models, focusing on the complete analytic trans-series. Delve into this advanced topic in condensed matter physics and quantum field theory through a comprehensive lecture by Z. Bajnok from the Wigner Institute. Gain insights into the mathematical techniques and theoretical frameworks used to analyze these complex systems, and understand how the full analytic trans-series contributes to our understanding of integrable models. Enhance your knowledge of integrability and its applications in modern physics during this in-depth, hour-long presentation.