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The critical behaviour of Ising spins on 2D Regge lattices

C. Holm·W. Janke
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Abstract

We performed a high statistics simulation of Ising spins coupled to 2D quantum gravity on toroidal geometries. The tori were triangulated using the Regge calculus approach and contained up to $512^2$ vertices. We used a constant area ensemble with an added $R^2$ interaction term, employing the $dl/l$ measure. We find clear evidence that the critical exponents of the Ising phase transition are consistent with the static critical exponents and do not depend on the coupling strength of the $R^2$ interaction term. We definitively can exclude for this type of model a behaviour as predicted by Boulatov and Kazakov [Phys. Lett. {\bf B186}, 379 (1987)] for Ising spins coupled to dynamically triangulated surfaces.

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C. Holm, W. Janke. 1994-06-27. The critical behaviour of Ising spins on 2D Regge lattices. https://doi.org/10.1016/0370-2693(94)91405-2

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