Vortex-loop crinkling in the three-dimensional XY model: numerical evidence in support of an ansatz

Chattopadhyay, Biplab ; Mahato, Mangal C. ; Shenoy, Subodh R. (1993) Vortex-loop crinkling in the three-dimensional XY model: numerical evidence in support of an ansatz Physical Review B: Condensed Matter and Materials Physics, 47 (22). pp. 15159-15169. ISSN 1098-0121

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Official URL: http://prb.aps.org/abstract/PRB/v47/i22/p15159_1

Related URL: http://dx.doi.org/10.1103/PhysRevB.47.15159

Abstract

A scaling theory for the three-dimensional (3D) XY ferromagnet was previously proposed, in terms of directed vortex loops of average diameter a=el, and core size ac(l). An ansatz was made for the loop self-energy from a 1/R potential, E~a ln[a/ac(l)]→a lnK−xl, where Kl is the screened coupling and x≃=0.6 the self-avoiding random-walk exponent. Here, the central role of the core-size ansatz in producing known 3D XY exponents is brought out in numerical solutions of the scaling equations. We then relate the cutoff ac(l) to radial fluctuations around the mean radius a/2, and provide partial numerical support for the ansatz by computer-generated vortex-loop configurations. A Flory-type polymer argument for the core size ac(l) is given.

Item Type:Article
Source:Copyright of this article belongs to The American Physical Society.
ID Code:46020
Deposited On:30 Jun 2011 09:58
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