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

Journal Article · Mon Nov 01 04:00:00 EST 1993 · Journal of Statistical Physics; (United States)

DOI:https://doi.org/10.1007/BF01054349· OSTI ID:7206864

Kiskis, J ^[1]; Narayanan, R ^[2]; Vranas, P ^[3]

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1. Univ. of California, Davis, CA (United States)
2. Rutgers Univ., Piscataway, NJ (United States)
3. Florida State Univ., Tallahassee, FL (United States)

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.

• OSTI ID: 7206864
• Journal Information: Journal of Statistical Physics; (United States), Journal Name: Journal of Statistical Physics; (United States) Vol. 73:3-4; ISSN JSTPBS; ISSN 0022-4715
• Country of Publication: United States
• Language: English

Related Subjects

662110* -- General Theory of Particles & Fields-- Theory of Fields & Strings-- (1992-)
72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS
CONSTRUCTIVE FIELD THEORY
DYNAMICAL GROUPS
FIELD THEORIES
HAUSDORFF SPACE
LIE GROUPS
MATHEMATICAL SPACE
MECHANICS
O GROUPS
QUANTUM FIELD THEORY
RANDOMNESS
SPACE
STATISTICAL MECHANICS
STOCHASTIC PROCESSES
SYMMETRY GROUPS