  We study three possible ways to circumvent the sign problem in the O(3)
nonlinear sigma model in 1+1 dimensions. We compare the results of the worm
algorithm to complex Langevin and multiparameter reweighting. Using the worm
algorithm, the thermodynamics of the model is investigated, and continuum
results are shown for the pressure at different $\mu/T$ values in the range
$0-4$. By performing $T=0$ simulations using the worm algorithm the Silver
Blaze phenomenon is reproduced. Regarding the complex Langevin, we test various
implementations of discretizing the complex Langevin equation. We found that
the exponentialized Euler discretization of the Langevin equation gives wrong
results for the action and the density at low $T/m$. By performing continuum
extrapolation we found that this discrepancy does not disappear and depends
slightly on temperature. The discretization with spherical coordinates perform
similarly at low $\mu/T$, but goes wrong also at some higher temperatures at
high $\mu/T$. However, a third discretization that uses a constraining force to
achieve the $\phi^2 = 1$ condition gives correct results for the action, but
wrong results for the density at low $\mu/T$.
