Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)In the present work we analyze the quantum phase transition (QPT) in the N-atom Jaynes-Cummings model (NJCM) with an additional symmetry breaking interaction term in the Hamiltonian. We show that depending on the type of symmetry breaking term added the transition order can change or not and also the fixed point associated to the classical analogue of the Hamiltonian can bifurcate or not. We present two examples of symmetry broken Hamiltonians and discuss based on them. the interconnection between the transition order, appearance of bifurcation and the behavior of the entanglement. (C) 2008 Elsevier B.V. All rights reserved.3723455645568Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)