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Title: The Hausdorff dimension of random walks and the correlation length critical exponent in Euclidean field theory

Abstract

The authors study the random walk representation of the two-point function in statistical mechanics models near the critical point. Using standard scaling arguments, the authors show that the critical exponent v describing the vanishing of the physical mass at the critical point is equal to v[sub [theta]]/d[sub w], where d[sub w] is the Hausdorff dimension of the walk, and v[sub [theta]] = [var phi], where [var phi] is the crossover exponent known in the context of field theory. This implies that the Hausdorff dimension of the walk is [var phi]/v for O(N) models. 3 refs.

Authors:
 [1];  [2];  [3]
  1. Univ. of California, Davis, CA (United States)
  2. Rutgers Univ., Piscataway, NJ (United States)
  3. Florida State Univ., Tallahassee, FL (United States)
Publication Date:
OSTI Identifier:
7206864
Resource Type:
Journal Article
Journal Name:
Journal of Statistical Physics; (United States)
Additional Journal Information:
Journal Volume: 73:3-4; Journal ID: ISSN 0022-4715
Country of Publication:
United States
Language:
English
Subject:
72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS; CONSTRUCTIVE FIELD THEORY; HAUSDORFF SPACE; STOCHASTIC PROCESSES; O GROUPS; RANDOMNESS; STATISTICAL MECHANICS; DYNAMICAL GROUPS; FIELD THEORIES; LIE GROUPS; MATHEMATICAL SPACE; MECHANICS; QUANTUM FIELD THEORY; SPACE; SYMMETRY GROUPS; 662110* - General Theory of Particles & Fields- Theory of Fields & Strings- (1992-)

Citation Formats

Kiskis, J, Narayanan, R, and Vranas, P. The Hausdorff dimension of random walks and the correlation length critical exponent in Euclidean field theory. United States: N. p., 1993. Web. doi:10.1007/BF01054349.
Kiskis, J, Narayanan, R, & Vranas, P. The Hausdorff dimension of random walks and the correlation length critical exponent in Euclidean field theory. United States. https://doi.org/10.1007/BF01054349
Kiskis, J, Narayanan, R, and Vranas, P. 1993. "The Hausdorff dimension of random walks and the correlation length critical exponent in Euclidean field theory". United States. https://doi.org/10.1007/BF01054349.
@article{osti_7206864,
title = {The Hausdorff dimension of random walks and the correlation length critical exponent in Euclidean field theory},
author = {Kiskis, J and Narayanan, R and Vranas, P},
abstractNote = {The authors study the random walk representation of the two-point function in statistical mechanics models near the critical point. Using standard scaling arguments, the authors show that the critical exponent v describing the vanishing of the physical mass at the critical point is equal to v[sub [theta]]/d[sub w], where d[sub w] is the Hausdorff dimension of the walk, and v[sub [theta]] = [var phi], where [var phi] is the crossover exponent known in the context of field theory. This implies that the Hausdorff dimension of the walk is [var phi]/v for O(N) models. 3 refs.},
doi = {10.1007/BF01054349},
url = {https://www.osti.gov/biblio/7206864}, journal = {Journal of Statistical Physics; (United States)},
issn = {0022-4715},
number = ,
volume = 73:3-4,
place = {United States},
year = {Mon Nov 01 00:00:00 EST 1993},
month = {Mon Nov 01 00:00:00 EST 1993}
}