Correlation functions and the Goldstone picture for the hierarchical classical vector model at low temperatures in three or more dimensions |
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Authors: | Ricardo Schor Michael O'Carroll |
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Institution: | (1) Departamento de Física, ICEx, UFMG, Universidade Federal de Minas Gerais, 31270 Belo Horizonte, M.G., Brazil;(2) Present address: Department of Mathematics, Rutgers University, Hill Center, Busch Campus, 08903 New Brunswick, New Jersey |
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Abstract: | Low-temperature properties of the one-and two-point correlation functions are obtained for the pure state classical vector model in a hierarchical formulation. We consider theZ
d lattice model (d3) where the single-site spin variableR
v
has a density proportional to
for large. We obtain the pure state one- and two-point functions by introducing a uniform magnetic field which goes to zero as the volume goes to infinity. Using renormalization group methods, we generate a sequence of effective actions and spin variable and determine the spontaneous magnetization (one-point function parallel to the field). We confirm the Goldstone picture by showing that the truncated two-point function has the canonical massless decay x–y–(d–2)
x,yZd in the directions perpendicular to the field. We show a faster decay in the parallel direction and for larged that the decay is x-y–(d+2).Research support by CNPq, Brazil. |
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Keywords: | Hierarchical classical vector model Goldstone picture infrared asymptotic freedom renormalization group method correlation functions |
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