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Criticality and conformality in the random dimer model

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Sergio Caracciolo, R Fabbricatore, M Gherardi, R Marino, Giorgio Parisi, Gabriele Sicuro

Original languageEnglish
Article number042127
JournalPHYSICAL REVIEW E
Volume103
Issue number4
DOIs
Accepted/In press5 Apr 2021
Published16 Apr 2021

Bibliographical note

Funding Information: The authors are grateful to Carlo Lucibello for providing them his preliminary data about the REMP. The authors would like to thank Bertrand Duplantier, Scott Kirkpatrick, Nicolas Macris, and Andrea Sportiello for useful discussions. The research of G.P. and G.S. has been supported by the Simons Foundation (Grant No. 454949). R.M. has been supported by Swiss National Foundation Grant No. 200021E 17554. Publisher Copyright: © 2021 American Physical Society. Copyright: Copyright 2021 Elsevier B.V., All rights reserved.

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Abstract

In critical systems, the effect of a localized perturbation affects points that are arbitrarily far from the perturbation location. In this paper, we study the effect of localized perturbations on the solution of the random dimer problem in two dimensions. By means of an accurate numerical analysis, we show that a local perturbation of the optimal covering induces an excitation whose size is extensive with finite probability. We compute the fractal dimension of the excitations and scaling exponents. In particular, excitations in random dimer problems on nonbipartite lattices have the same statistical properties of domain walls in spin glass. Excitations produced in bipartite lattices, instead, are compatible with a loop-erased self-avoiding random walk process. In both cases, we find evidence of conformal invariance of the excitations that is compatible with SLEκ with parameter κ depending on the bipartiteness of the underlying lattice only.

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