NEW CRITICALITY OF 1D FERMIONS

One-dimensional massive quantum particles [or (1 + 1)-dimensional rand om walks] with short-ranged multiparticle interactions are studied by exact renormalization group methods. With repulsive pair forces, such particles are known to scale as free fermions. With finite m-body forc es (m = 3,4,...) a critical instability is found, indicating the trans ition to a fermionic bound state. These unbinding transitions represen t new universality classes of interacting fermions relevant to polymer and membrane systems. Implications for massless fermions, e.g., in th e Hubbard model, are also noted.