Gabriele Bandini — SISSA #
XY model with vision cone: nonreciprocal vs reciprocal interactions on the lattice #
In this work we investigate the possibilities and the shortcomings that arise when implementing nonreciprocal and reciprocal interaction on a lattice model, in particular on a classical XY model with a vision cone. Reference [1] showed that adding a vision cone in a nonreciprocal fashion, i.e. featuring a selfish energy (and not a total energy functional) with non-symmetric couplings, leads to a non-equilibrium state with a long-range order (LRO) phase at low temperatures. Here we consider two reciprocal variation of such a model: (i) the first one is characterized by a total energy functional obtained as the sum of the selfish energies, and whose equilibrium state still has a long-range order, thus showing that such feature is to be ascribed to the vision cone nature of the interactions and not to their nonreciprocity; (ii) the second one considers a particular energy functional with symmetric couplings, for which we introduce the concept of redundant bonds, that leads to a stable quasi-long-range order (QLRO) phase and to an order-by-disorder transition