The critical exponents of crystalline random surfaces |
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| Affiliation: | 1. Center for Molecular Cardiology, University of Zurich, Schlieren, Switzerland;2. First Clinic of Internal Medicine, Department of Internal Medicine, University of Genoa, Genoa, Italy;3. Cardiovascular Research Program ICCC, IR-IIB Sant Pau, Hospital de la Santa Creu i Sant Pau, CiberCV–Institute Carlos III, Barcelona, Spain;4. IRCCS Ospedale Policlinico San Martino Genoa–Italian Cardiovascular Network, Genoa, Italy;5. Royal Brompton and Harefield Hospitals and Imperial College, London, United Kingdom;6. Division of Cardiovascular Medicine, Department of Medicine, Brigham and Women’s Hospital, Harvard Medical School, Boston, Massachusetts, USA;7. University Heart Center, Department of Cardiology, University Hospital Zurich, Zurich, Switzerland;8. Department of Research and Education, University Hospital Zurich, Zurich, Switzerland;1. National Research Center of Pumps, Jiangsu University, Zhenjiang, 212013, China;2. Institute of Fluid Engineering Equipment Technology, Jiangsu University, Zhenjiang, 212009, China;3. College of Mechanical Engineering, Nantong University, Nantong, 226019, China;4. School of Energy and Power Engineering, Jiangsu University, Zhenjiang, 212013, China;5. Department of Mechanical Engineering & Materials Science, Washington University in St. Louis, St. Louis, MO, 63130, USA |
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| Abstract: | We report on a high statistics numerical study of the crystalline random surface model with extrinsic curvature on lattices of up to 642 points. The critical exponents at the crumpling transition are determined by a number of methods all of which are shown to agree within estimated errors. The correlation length exponent is found to be ν = 0.71(5) from the tangent-tangent correlation function whereas we find ν = 0.73(6) by assuming finite size scaling of the specific heat peak and hyperscaling. These results imply a specific heat exponent α = 0.58(10); this is a good fit to the specific heat on a 642 lattice with a χ2 per degree of freedom of 1.7 although the best direct fit to the specific heat data yields a much lower value of a. We have measured the normal-normal correlation function in the crumpled phase and find that, within the accuracy of our simulations, the data can be described by a super-renormalizable field theory. |
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