Geodesic
Renormalization-Group Transformation in a~$2n$-Component Fermionic Hierarchical Model
Teoretičeskaâ i matematičeskaâ fizika, Tome 146 (2006) no. 2, pp. 251-266

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We study the $2N$-component fermionic model on a hierarchical lattice and give explicit formulas for the renormalization-group transformation in the space of coefficients that determine a Grassmann-valued density of the free measure. We evaluate the inverse renormalization-group transformation. The de.nition of the renormalization-group fixed points reduces to a solution of a system of algebraic equations. We investigate solutions of this system for $N=1,2,3$. For $\alpha=1$, we prove an analogue of the central limit theorem for fermionic $2N$-component fields. We discover an interesting relation between renormalization-group transformations in bosonic and fermionic hierarchical models and show that one of these transformations is obtained from the other by replacing $N$ with $-N$.
Keywords: renormalization group, $N$-component fermionic fields, hierarchical models. 
@article{TMF_2006_146_2_a3,
     author = {R. G. Stepanov},
     title = {Renormalization-Group {Transformation} in a~$2n${-Component} {Fermionic} {Hierarchical} {Model}},
     journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
     pages = {251--266},
     publisher = {mathdoc},
     volume = {146},
     number = {2},
     year = {2006},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TMF_2006_146_2_a3/}
}
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R. G. Stepanov. Renormalization-Group Transformation in a~$2n$-Component Fermionic Hierarchical Model. Teoretičeskaâ i matematičeskaâ fizika, Tome 146 (2006) no. 2, pp. 251-266. http://geodesic.mathdoc.fr/item/TMF_2006_146_2_a3/