Abstract:
We consider a two-dimensional hierarchical lattice in which the vertices
of a square represent an elementary cell. In the generalized hierarchical model,
the distance between opposite vertices of a square differs from that
between adjacent vertices and is a parameter of the new model.
The Gaussian part of the Hamiltonian
of the 4-component generalized fermionic hierarchical model
is invariant
under the block-spin renormalization group transformation.
The transformation of the renormalization group in the space of coefficients,
which specify the Grassmann-valued density of the free measure, is explicitly
calculated as a homogeneous mapping of degree four in the two-dimensional
projective space.
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