An exactly solvable model is presented that exhibits a phase transition and that can be exactly described by Landau's phase transition theory. The model is used to elucidate the constructs and assumptions that go into the Landau theory, and also to illustrate the role of fluctuations near an instability in a finite system.

American Journal of PhysicsJan 1, 197211 citations

The RG method applied to an exactly solvable model of phase transitions

Yu. M. Ivanchenko, Alexander A. Lisyansky, Alexander E. Filippov

The renormalisation group (RG) method is applied to the investigation of an exactly solvable phase transition model in which only the interaction between fluctuations with equal and antiparallel momenta is taken into account. The RG equation for the model is derived, its exact solution and critical asymptotics are obtained. It is shown that direct calculation of the partition function and solution of the RG equation for the model lead to identical results.

Journal of Physics A Mathematical and GeneralJan 7, 19905 citations