Abstract
We study the phase diagram of the 3-matrix model. This model corresponds to the Blume-Emery-Griffiths (BEG) model on a random surface. The BEG model has parameters J and K which are the spin and the lattice-gas coupling respectively. If K = 0, it is the usual tri-critical Ising model. If K/J = 3, this model becomes the 3-state Potts model. These models are solved in the context of the Coulomb gas representation. The intermediate region K/J = 1 is equivalent to the 3-matrix chain model and we can solve it exactly using the orthogonal polynomial method. We find the 3rd order critical line on which the spin ordering phase transition occurs. This line ends at the 4th order critical point which corresponds to the tri-critical point of the BEG model. The phase diagram is quite similar to that of the BEG model on a regular lattice.
Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
