Ward's identity in critical dynamics |
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Authors: | Richard A. Ferrell Jayanta K. Bhattacharhjee |
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Affiliation: | (1) Center for Theoretical Physics, Department of Physics and Astronomy University of Maryland, 20742 College Park, Maryland;(2) Department of Physics, Indian Institute of Technology, Kanpur, 208016 U.P., India |
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Abstract: | We consider the relaxation of an order-parameter fluctuation of wave numberk in a system undergoing a second-order phase transition. In general, close to the critical point, wherek–1 –1 (the correlation length) the relaxation rate has a linear dependence on/k of the form (k, ) = (k, 0)x(1–a/k). In analogy with the use of Ward's identity in elementary particle physics, we show that the numerical coefficienta is readily calculated by means of a mass insertion. We demonstrate, furthermore, that this initial linear drop is the main feature of the full/k dependence of the scaling functionR–x(k,), wherex is the dynamic critical exponent andR=(k2+2)1/2 is the distance variable. |
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Keywords: | Ward's identity critical dynamics scaling function phase transition |
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