Random walk construction of spinor fields on a three-dimensional lattice |
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Affiliation: | 1. Department of Physics, Laser Laboratory, GJU S&T, Hisar, Haryana 125001, India;2. Department of Nano Science and Advanced Materials, Saurashtra University, Rajkot 360005, India;3. Materials Science Division, Inter-University Accelerator Center, Aruna Asaf Ali Marg, New Delhi 110067, India;4. Department of Physics & Centre for Interdisciplinary Research, University of Petroleum and Energy Studies (UPES), Dehradun, Uttarakhand 248007, India |
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Abstract: | Euclidean-invariant Klein-Gordon, Dirac and massive Chern-Simons field theories are constructed in terms of a random walk with a spin factor on a three-dimensional lattice. We exactly calculate the free energy and the correlation functions which allow us to obtain the critical diffusion constant and associated critical exponents. It is pointed out that these critical exponents do not satisfy the hyper-scaling relation but the scaling inequalities. We take the continuum limit of this theory on the basis of these analyses. We check the universality of the obtained results on other lattice structures such as the triclinic lattice and the body-centered lattice. |
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