Faculty of Physics - University of Bucharest

UNIVERSITY OF BUCHAREST
FACULTY OF PHYSICS

Guest
2024-11-21 20:36

HOME CONFERENCES SEARCH LOGIN NEW USER IMAGES

Conference: Bucharest University Faculty of Physics 2008 Meeting

Section: Theoretical Physics and Applied Mathematics Seminar

Title:

Spin correlation functions of the Ising model on the 3-12 lattice and the average numbers of triangles for the associated generalized Wheler-Widom model

Authors:

Radu P. Lungu

Affiliation:

University of Bucharest, Department of Physics, Chair of Theoretical Physics and Mathematics

E-mail

RaduPLungu@yahoo.com, lungu@barutu.fizica.unibuc.ro

Keywords:

Ising models, phase transitions

Abstract:

A generalized Wheeler-Widom model for a ternary solution is considered, in which the links of a honeycomb lattice are covered by rod-like molecules of types AA, BB, and AB; the molecular ends near a common site have three-body interactions, and also there are many internal states (bonding and non-bonding) for each molecular end. The model is equivalent to a spin-1/2 Ising model in a field, with two-spin and three-spin interactions on an associated 3-12 lattice that has sites at the positions of the molecular ends. The average number of molecules (AA, AB, and BB) and the average number of triangles (AAA, BBB, ABA, and BAB) of each type can be expressed as linear combinations of spin averages for the associated Ising model: the magnetization, the 2-spin correlation function for spins inside a triangle, the 2-spin correlation function for spins belonging to nearest neighboring triangles, and 3-spin correlation function for spins inside a triangle. Using transformation methods, the Ising model on the 3-12 lattice is itself equivalent to a simple spin-1/2 Ising model on the original lattice with a magnetic field and pure two-spin interactions. From this equivalence, the spin correlation functions of the Ising model on the 3-12 lattice can be expressed in terms of the magnetization and the 2-spin correlation function between nearest neighboring spins for the Ising model on the honeycomb lattice. The above specified spin correlation functions of the Ising model on the 3-12 lattice were calculated numerically for the states corresponding to phase transition, when in the associated molecular system occurs the coexistence between the AA-rich and BB-rich phases. Then, the plots of the average numbers of triangles of each types are obtained numerically. The results are particularized for the limiting case of binary system, when the system contains only AA and AB molecules, and the mole fraction of AB molecules vanishes.