In physics, particularly in quantum field theory and statistical mechanics, interactions among particles are often characterized by the types of terms in the Lagrangian or Hamiltonian that describe the system. A "quartic interaction" refers to a term in the theory that involves four fields or four particles interacting with each other simultaneously. Mathematically, a quartic interaction can take the form of a term in the Lagrangian that is proportional to the product of four fields.
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Phi-fourth theory has a scalar interaction . In four dimensions its coupling is classically marginal, and its one-loop four-point function receives bubble corrections in the three Mandelstam channels.