The main "poster child" for such argument is Phil Anderson's "More Is Different" paper published quite a while back. Now comes a paper that strengthen Anderson's assertion that More Really Is Different.
Gu et al. published a paper in which, using the 2D Ising model that simulates a cellular automata of magnetic spins.
Abstract: In 1972, P.W. Anderson suggested that ‘More is Different’, meaning that complex physical systems may exhibit behavior that cannot be understood only in terms of the laws governing their microscopic constituents. We strengthen this claim by proving that many macroscopic observable properties of a simple class of physical systems (the infinite periodic Ising lattice) cannot in general be derived from a microscopic description. This provides evidence that emergent behavior occurs in such systems, and indicates that even if a ‘theory of everything’ governing all microscopic interactions were discovered, the understanding of macroscopic order is likely to require additional insights.
A News and Views in Nature this week article reviewing this paper explains it a little bit clearer for those of us not familiar with these 2D computation and the intricacies of cellular automata.
In their study, Gu et al. mapped the dynamics of a certain CA into the lowest-energy (ground) states of Ising models. In this framework, Figure 1 can now be interpreted as a snapshot of a two-dimensional spatial lattice of spins. They grouped spins into blocks that encode the logic operations needed to produce universal computation in the corresponding CA. They then defined the 'prosperity', p, of two-state systems as "the probability that a randomly chosen cell at a random time step is live" (live meaning state 1).
Using the computational properties of the CA, Gu and colleagues were able to show that p is undecidable for infinite, periodic Ising systems. They argued that, as a consequence, many macroscopic properties of an Ising system, including the system's magnetization and degeneracy (number of independent configurations) at zero temperature, depend on p and hence are also undecidable. Because Ising models have been used to describe not only magnetic materials but also neural activity, protein folding and bird flocking, the consequences of Gu and colleagues' results transcend both computer science and physics.
Nice stuff! This would be another compelling argument against reductionism and the fallacy of the "Theory of Everything".
 M. Gu et al., Physica D: Nonlinear Phenomena, v.238, p.835 (2009). Also see the arXiv version here.
 P.M. Binder Nature v.459, p.332 (2009).