On the short distance behavior of the critical Ising model perturbed by a magnetic field |
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| Institution: | 1. CEA-Saclay, Service de Physique Théorique, F-91191 Gif-sur-Yvette Cedex, France;2. Dipartimento di Fisica, Università di Genova, Via Dodecaneso, 33, 16146 Genova, Italy;3. Istituto Nazionale di Fisica Nucleare, Sez. Genova, Via Dodecaneso, 33, 16146 Genova, Italy;1. Key Laboratory of Solid Waste Treatment and Resource Recycle, Ministry of Education, Southwest University of Science and Technology, Mianyang 621010, China;2. State Key Laboratory for Environment-friendly Energy Materials, Southwest University of Science and Technology, Mianyang 621010, China;3. State Key Laboratory of Complex Nonferrous Metal Resources Clean Utilization, Kunming University of Science and Technology, Kunming 650093, China;1. Longhua Hospital, Shanghai University of Traditional Chinese Medicine, Shanghai, China;2. Shanghai Institute of Materia Medica, Chinese Academy of Sciences, Shanghai, China;1. Centre for Health Protection, National Institute for Public Health and the Environment (RIVM), Antonie van Leeuwenhoeklaan 9, 3721 MA Bilthoven, the Netherlands;2. Division of Human Nutrition and Health, Wageningen University, Stippeneng 4, 6708 WE Wageningen, the Netherlands;1. Department of Internal Medicine, University Hospital of Cologne, 50931 Cologne, Germany;2. Cologne Excellence Cluster on Cellular Stress Response in Aging-Associated Diseases, University of Cologne, 50674 Cologne, Germany;1. Oncology Unit, Oncology Department, ASST Ospedale di Cremona, Cremona, Italy;2. Oncology Unit, Oncology Department, ASST Bergamo Ovest, Treviglio, Bergamo, Italy;3. Surgery Unit, ASST Bergamo Ovest, Treviglio, Bergamo, Italy;4. Pathology Unit, ASST Bergamo Ovest, Treviglio, Bergamo, Italy |
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| Abstract: | We apply here a recently developed approach to compute the short distance corrections to scaling for the correlators of all primary operators of the critical two-dimensional Ising model in a magnetic field. The essence of the method is the fact that if one deals with OPE Wilson coefficients instead of correlators, all-order IR safe formulas can be obtained for the perturbative expansion with respect to the magnetic field. This approach yields in a natural way the expected fractional powers of the magnetic field, which are clearly absent in the naive perturbative expression for correlators. The technique of the Mellin transform has been used to compute the IR behavior of the regularized integrals. As a corollary of our results, by comparing the existing numerical data for the lattice model we give an estimate of the vacuum expectation value of the energy operator of the continuous theory. |
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