Artículos de revistas
Hierarchical spherical model from a geometric point of view
Fecha
2008Registro en:
JOURNAL OF STATISTICAL PHYSICS, v.132, n.5, p.811-838, 2008
0022-4715
10.1007/s10955-008-9568-1
Autor
Marchetti, Domingos Humberto Urbano
Conti, William Remo Pedroso
Guidi, Leonardo Fernandes
Institución
Resumen
A continuous version of the hierarchical spherical model at dimension d=4 is investigated. Two limit distributions of the block spin variable X(gamma), normalized with exponents gamma = d + 2 and gamma=d at and above the critical temperature, are established. These results are proven by solving certain evolution equations corresponding to the renormalization group (RG) transformation of the O(N) hierarchical spin model of block size L(d) in the limit L down arrow 1 and N ->infinity. Starting far away from the stationary Gaussian fixed point the trajectories of these dynamical system pass through two different regimes with distinguishable crossover behavior. An interpretation of this trajectories is given by the geometric theory of functions which describe precisely the motion of the Lee-Yang zeroes. The large-N limit of RG transformation with L(d) fixed equal to 2, at the criticality, has recently been investigated in both weak and strong (coupling) regimes by Watanabe (J. Stat. Phys. 115:1669-1713, 2004) . Although our analysis deals only with N = infinity case, it complements various aspects of that work.