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The Ising Model on a Quenched Ensemble of c=−5 Gravity Graphs

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Abstract

We study with Monte Carlo methods an ensemble of c=−5 gravity graphs, generated by coupling a conformal field theory with central charge c=−5 to two-dimensional quantum gravity. We measure the fractal properties of the ensemble, such as the string susceptibility exponent γ s and the intrinsic fractal dimension d H. We find γ s=−1.5(1) and d H=3.36(4), in reasonable agreement with theoretical predictions. In addition, we study the critical behavior of an Ising model on a quenched ensemble of the c=−5 graphs and show that it agrees, within numerical accuracy, with theoretical predictions for the critical behavior of an Ising model coupled dynamically to two-dimensional quantum gravity, with a total central charge of the matter sector c=−5.

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Authors and Affiliations

  1. The Niels Bohr Institute, DK-2200, Copenhagen, Denmark

    K. N. Anagnostopoulos

  2. Institute of Computer Science, Jagellonian University, 30-072, Krakow, Poland

    P. Bialas

  3. Fakultät für Physik, Universität Bielefeld, D-33615, Bielefeld, Germany

    G. Thorleifsson

Authors
  1. K. N. Anagnostopoulos
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  2. P. Bialas
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  3. G. Thorleifsson
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Anagnostopoulos, K.N., Bialas, P. & Thorleifsson, G. The Ising Model on a Quenched Ensemble of c=−5 Gravity Graphs. Journal of Statistical Physics 94, 321–345 (1999). https://doi.org/10.1023/A:1004583901498

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