ICM 1998, Berlin, Aug. 18–27

Abstracts of Short Communications and Posters

Section:

11. Mathematical Physics

1991 MS Classification: 81T27, 82B27, 82B28 Missarov Moukadas, Kazan State University, Russia Critical phenomena and continuum limit in the hierarchical fermionic model The hierarchical fermionic model is defined as a model with 4-component Grassmann-valued spins on the hierarchical lattice with self-similar Gaussian part and local potential r(ψ̄_{1}ψ_{1}+ψ̄_{2}ψ_{2})+gψ̄_{1}ψ_{1}ψ̄_{2}ψ_{2}. The renormalization group transformation is given by rational map in the plane (r, g). This dynamical system has a wide variety of dynamical phenomena. We discuss intricate critical behaviour and continuum limit problem in this model. Reference: E. Yu. Lerner and M. D. Missarov, Global flow of renormalization group and thermodynamic limit in the hierarchical fermionic model, Teor. i Mat. Fiz. , 107 (1996), 201–212 (in russian).