Fixed-point structure and effective fractional dimensionality for O(N) models with long-range interactions
Year: 2015
Authors: Defenu N., Trombettoni A., Codello A.
Autors Affiliation: SISSA, I-34136 Trieste, Italy; CNR IOM DEMOCRITOS Simulat Ctr, I-34136 Trieste, Italy; Ist Nazl Fis Nucl, Sez Trieste, I-34136 Trieste, Italy; Univ Southern Denmark, Origins CP3, DK-5230 Odense M, Denmark; Univ Southern Denmark, Danish Inst Adv Study, DK-5230 Odense M, Denmark.
Abstract: We study, by renormalization group methods, O(N) models with interactions decaying as power law with exponent d + sigma. When only the long-range momentum term p(sigma) is considered in the propagator, the critical exponents can be computed from those of the corresponding short-range O(N) models at an effective fractional dimension D-eff. Neglecting wave function renormalization effects the result for the effective dimension is D-eff = 2d/sigma, which turns to be exact in the spherical model limit (N -> 8). Introducing a running wave function renormalization term the effective dimension becomes instead D-eff = (2-eta SR)d/sigma . The latter result coincides with the one found using standard scaling arguments. Explicit results in two and three dimensions are given for the exponent nu. We propose an improved method to describe the full theory space of the models where both short-and long-range propagator terms are present and no a priori choice among the two in the renormalization group flow is done. The eigenvalue spectrum of the full theory for all possible fixed points is drawn and a full description of the fixed-point structure is given, including multicritical long-range universality classes. The effective dimension is shown to be only approximate, and the resulting error is estimated.
Journal/Review: PHYSICAL REVIEW E
Volume: 92 (5) Pages from: 52113-1 to: 52113-11
More Information: We are very grateful to G. Gori and M. A. Rajabpour for many useful discussions during various stages of the work. The CP3-Origins center is partially funded by the Danish National Research Foundation, Grant No. DNRF90.KeyWords: Critical Exponents; Phase-transitionDOI: 10.1103/PhysRevE.92.052113Citations: 68data from “WEB OF SCIENCE” (of Thomson Reuters) are update at: 2024-10-20References taken from IsiWeb of Knowledge: (subscribers only)