  Patterns of avoidance, adjacency, and association in complex systems design
emerge from the system's underlying logical architecture (functional
relationships among components) and physical architecture (component physical
properties and spatial location). Understanding the physical--logical
architecture interplay that gives rise to patterns of arrangement requires a
quantitative approach that bridges both descriptions. Here, we show that
statistical physics reveals patterns of avoidance, adjacency, and association
across sets of complex, distributed system design solutions. Using an example
arrangement problem and tensor network methods, we identify several phenomena
in complex systems design, including placement symmetry breaking, propagating
correlation, and emergent localization. Our approach generalizes
straightforwardly to a broad range of complex systems design settings where it
can provide a platform for investigating basic design phenomena.
