  By using random matrix models we uncover a connection between the low energy
sector of four dimensional QCD at finite volume and the Heisenberg XX model in
a 1d spin chain. This connection allows to relate crucial properties of QCD
with physically meaningful properties of the spin chain, establishing a
dictionary between both worlds. We predict for the spin chain a third-order
phase transition and a Tracy-Widom law in the transition region. We postulate
that this dictionary goes beyond the particular example analyzed here and can
be applied to other QFT and spin chain models. We finally comment on possible
numerical implications of the connection as well as on possible experimental
implementations.
