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arXiv · hep-lat/9812015

Connected Correlators in Quantum Gravity

J. Ambjorn·P. Bialas·J. Jurkiewicz
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Abstract

We discuss the concept of connected, reparameterization invariant matter correlators in quantum gravity. We analyze the effect of discretization in two solvable cases: branched polymers and two-dimensional simplicial gravity. In both cases the naively defined connected correlators for a fixed volume display an anomalous behavior, which could be interpreted as a long-range order. We suggest that this is in fact only a highly non-trivial finite-size effect and propose an improved definition of the connected correlator, which reduces the effect. Using this definition we illustrate the appearance of a long-range spin order in the Ising model on a two-dimensional random lattice in an external magnetic field $H$, when $H \to 0$ and $β=β_C$.

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J. Ambjorn, P. Bialas, J. Jurkiewicz. 1998-12-18. Connected Correlators in Quantum Gravity. https://doi.org/10.1088/1126-6708%2F1999%2F02%2F005

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