We study a non-unitary spin chain with orthosymplectic symmetry that generalizes the O(N) model to any positive or negative integer N. The lack of unitarity allows a stable massless Goldstone phase to appear, otherwise forbidden by the Mermin-Wagner theorem, that is described by a supersphere sigma model. On the 2D lattice it is represented as a dense loop model with loop weight N in which crossings are allowed. Unlike the usual O(N) loop model, the presence of crossings makes the model flow to a different regime where correlations involve logarithms. We compute these logarithmic critical exponents with field theory and the Bethe ansatz.