Ising (anti-)ferromagnet on dynamical triangulations and quadrangulations

Details Ising (anti-)ferromagnet on dynamical triangulations and quadrangulations Ising (anti-)ferromagnet on dynamical triangulations and quadrangulations

1993-07-20

arxiv.org/abs/hep-th/9307125v1

Phys.Lett. B314 (1993) 69-73

Physics

High Energy Physics

High Energy Physics - Theory

5 pages, latex

Scientific paper

10.1016/0370-2693(93)91323-F

We write down matrix models for Ising spins with zero external field on the vertices of dynamical triangulated random surfaces (DTRS) and dynamically quadrangulated random surfaces (DQRS) and compare these with the standard matrix model approach which places the spins on the dual $\phi^3$ and $\phi^4$ graphs. We show that the critical temperatures calculated in the DTRS and DQRS models agree with those deduced from duality arguments in the standard approach. Using the DQRS model we observe that the Ising antiferromagnet still undergoes a phase transition to a Neel (checkerboard) ordered ground state which is absent because of frustration in the other cases.

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