Combinatorics and physics ice-type model is six vertex model with domain wall boundary conditions. Combinatorics and physics Combinatorial physics or physical combinatorics is the area of interaction between physics and combinatorics. "Combinatorial Physics is an emerging area which unites combinatorial and discrete mathematical techniques applied to theoretical physics, especially Quantum Theory.". "Physical combinatorics might be defined naively as combinatorics guided by ideas or insights from physics". Combinatorics has always played an important role in quantum field theory and statistical physics. However, combinatorial physics only emerged as a specific field after a seminal work by Alain Connes and Dirk Kreimer, showing that the renormalization
Yukawa interaction explained by the fact that the Yukawa particle has spin zero and even spin always results in an attractive potential. The negative sign of the exponential gives the interaction an effectively finite range, so that particles at great distances will hardly interact any longer (interaction forces drop off exponentially with increasing separation). Now suppose that the potential formula_7 has a minimum not at formula_18 but at some non-zero value formula_19. This can happen, for example, with a potential form such as formula_20 with formula_9 set to an imaginary value. In this case, the Lagrangian exhibits spontaneous symmetry breaking. This is