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Perturbative expansions in many physical systems yield 'only' asymptotic series which are not even Borel resummable. Interestingly, the corresponding ambiguities point to nonperturbative physics. We numerically verify this renormalon mechanism for the first time in two-dimensional sigma models, that, like four-dimensional gauge theories, are asymptotically free and generate a strong scale through dimensional transmutation. We perturbatively expand the energy through a numerical version of stochastic quantization. In contrast to the first energy coefficients, the high order coefficients are independent on the rank of the model. Technically, they require a sophisticated analysis of finite volume effects and the continuum limit of the discretized model. Although the individual coefficients do not grow factorially (yet), but rather decrease strongly, the ratio of consecutive coefficients clearly obey the renormalon asymptotics., Comment: Published version, updated references, minor text changes, 13 pages, 10 figures, REVTeX style

In general, perturbative expansions of observables in powers of the coupling constant in quantum field theories are asymptotic series. In many cases it is possible to apply resummation techniques to assign a unique finite value to an asymptotic series, but a particular pattern of divergence, the so-called renormalon, gives rise to non-perturbative ambiguities. The framework of Numerical Stochastic Perturbation Theory (NSPT), based on stochastic quantisation and the perturbative expansion of lattice fields, makes it possible to compute coefficients of perturbative series on the lattice. In this work we report on an NSPT study of asymptotically free sigma models, namely the Principal Chiral Model and the $\text{CP}{(N-1)}$ model. We present results for a lattice computation of the expansion coefficients of the energy density and discuss signatures of renormalons., Comment: 7 pages, PoS style, to appear in the proceedings of the Lattice 2018 conference (22-28 July 2018, Michigan State University, East Lansing, Michigan, USA)