Andrea Ladiana

The exact Laplacian spectrum of the Berker–Ostlund diamond lattice

We derive, in closed form, the complete spectrum of the combinatorial Laplacian L(L) on the level- L Berker–Ostlund diamond hierarchical lattice DL(b) with branching parameter b⩾2. Because the vertex degree grows exponentially under inflation, the renormalized eigenvalue equation is not a Laplacian at the coarser scale...