Phase structure of the linear σ model in ${\mathit{R}}^{1+1}$

The phase structure of the two-dimensional linear σ model is investigated within the method based on canonical transformations and the renormalization group formalism. The phase diagram in the (Y,G) plane is constructed, where Y and G are the Yukawa and boson self-interaction coupling constants. The Hamiltonians describing the system in each phase are obtained. It is shown that the contribution of pseudoscalar fields diminishes the vacuum energy density in the phase with broken chiral symmetry. This results in a rather complicated phase structure of the linear σ model. The most representative features of the phase picture are the dynamical breaking of chiral symmetry for an arbitrary small Yukawa coupling and the presence of critical and triple points in the phase diagram.