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Study the phase transition in binary mixture

Basing on the Cornwall-Jackiw-Tomboulis (CJT) effective action approach, a theoretical formalism is established to study the Phase Transition in a binary mixture. The effective potential, which preserves the Goldstone theorem, is found in the Hartree-Fock (HF) approximation. This quantity is then used to consider the equation of state and the phase transition of the system. | JOURNAL OF SCIENCE OF HNUE Natural Sci. 2010 Vol. 55 No. 6 pp. 3-13 STUDY THE PHASE TRANSITION IN BINARY MIXTURE Le Viet Hoa Hanoi National University of Education To Manh Kien Xuan Mai High School Chuong My Hanoi Pham The Song Tay Bac University E-mail hoalv@yahoo.com Abstract. Basing on the Cornwall-Jackiw-Tomboulis CJT effective ac- tion approach a theoretical formalism is established to study the Phase Transition in a binary mixture. The effective potential which preserves the Goldstone theorem is found in the Hartree-Fock HF approximation. This quantity is then used to consider the equation of state and the phase transition of the system. Keywords Phase Transition binary equation of state. 1. Introduction In recent years there have been a lot of experimental works dealing with phase transition of systems composed of two distinct species of atoms 1-3 . The typical experiments were performed with atoms of 87 Rb in two different hyperfine states F 1 mf 1i and F 2 mf 1i which behave as two completely distinguishable species 1 because the hyperfine splitting is much larger than any other relevant energy scale in the system. The multicomponent phase transition is not a simple extension of the single component phase transition. There arise many novel phenomena such as the quantum tunnelling of spin domain 2 vortex configuration 1 phase segregation of binary mixture 3 and so on. In this article a theoretical formalism for studying phase transition in the global U 1 U 1 model is formulated by means of the CJT effective action 4 combining with the gapless HF resummation 5 . We then have obtained the effective potential in the HF approximation which respects the Goldstone theorem. 3 Le Viet Hoa To Manh Kien and Pham The Song The paper is organized as follows. In Section 2 we derive the desired effective potential. Section 3 is devoted to the physical property study of binary mixture. The conclusion and outlook are presented in Section 4. 2. Effective potential in HF .