  Non-trivial critical models in 2D with central charge c=0 are described by
Logarithmic Conformal Field Theories (LCFTs), and exhibit in particular mixing
of the stress-energy tensor with a "logarithmic" partner under a conformal
transformation. This mixing is quantified by a parameter (usually denoted b),
introduced in [V. Gurarie, Nucl. Phys. B 546, 765 (1999)], and which was first
thought to play the role of an "effective" central charge. The value of b has
been determined over the last few years for the boundary versions of these
models: $b_{\rm perco}=-5/8$ for percolation and $b_{\rm poly} = 5/6$ for
dilute polymers. Meanwhile, the existence and value of $b$ for the bulk theory
has remained an open problem. Using lattice regularization techniques we
provide here an "experimental study" of this question. We show that, while the
chiral stress tensor has indeed a single logarithmic partner in the chiral
sector of the theory, the value of b is not the expected one: instead, b=-5 for
both theories. We suggest a theoretical explanation of this result using
operator product expansions and Coulomb gas arguments, and discuss the physical
consequences on correlation functions. Our results imply that the relation
between bulk LCFTs of physical interest and their boundary counterparts is
considerably more involved than in the non-logarithmic case.
