Source
Koch-Janusz and Ringel (2017; Nature Physics 2018), LIT-873, read in NOTE-674. The abstract and closing discussion present the RSMI algorithm as a way to find relevant degrees of freedom without prior knowledge of them, and so as a route to renormalization in systems whose variables are not known.
What is asserted
That maximizing the mutual information between a block’s coarse variable and the environment beyond a buffer is a general criterion for the renormalization-group-relevant variables, and not only one that agrees with renormalization where its variables were already known. The authors also contrast it with coarse-grainings fitted to reproduce the data distribution, which on their noisy dimer data coupled to the noise.
What the record holds toward it
THEORY-194, Active, is the measured part: on the 2D Ising and noisy 2D dimer models the criterion recovered Kadanoff block spins and the dimers’ low-momentum electric fields, and iterated on Ising samples it located the critical point to about 1% with ν ≈ 1.0 ± 0.15. Every case had a known answer. The equivalence with a compact, short-ranged effective Hamiltonian is proved only for 1D and quasi-1D chains. Whether the criterion finds the variables where they are unknown is what QUESTION-232 asks; this THEORY is the proposed answer.
What this does not say
- Not that distribution-fitting coarse-grainings always fail. One dataset shows they need not succeed.
- Not that the criterion is computable at scale; the published runs are small lattices.
What would confirm or reject it
It is confirmed by the promote_when: a system with unknown relevant variables where the iterated criterion gives critical exponents matching an independent method, or a proof of short-ranged effective couplings in two or more dimensions. It is in trouble if, on such a system, the information-maximizing variables give a flow whose exponents disagree with an independent determination, or an effective Hamiltonian that is not short-ranged.