Central Limit Theorem for the hierarchical O(N) Heisenberg model at criticality and the role of the N -> infinity limit for the Lee-Yang zeros´s dynamics

Author(s)

William Remo Pedroso Conti

• Document type: Master's Dissertation
• Press: São Paulo.
• Institution: Universidade de São Paulo (USP). Instituto de Física (IF/SBI)
• Defense date: 2008-06-11

Examining board members

Domingos Humberto Urbano Marchetti; Paulo Domingos Cordaro; Walter Felipe Wreszinski

• Advisor: Domingos Humberto Urbano Marchetti

Abstract

In this work we stablish the Central Limit Theorem for the hierarchical O(N) Heisenberg model at criticality via partial differential equation in the limit N -> infinity. For simplicity we only treat the d = 4 case but the theorem is still valid for d > 4. By studying a given partial differential equation (PDE) we determine for any d > 2 the critical inverse temperature of the continuum hierarchical spherical model, and we show a connection between criticality and the fixed point of PDE. By means of a geometric analysis of the critical trajectory we obtain some informations about Lee-Yang zeros´s dynamics and distribution. (AU)