The Hausdorff dimension of random walks and the correlation length critical exponent in Euclidean field theory
Journal Article
·
· Journal of Statistical Physics; (United States)
- Univ. of California, Davis, CA (United States)
- Rutgers Univ., Piscataway, NJ (United States)
- 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), Vol. 73:3-4; ISSN 0022-4715
- Country of Publication:
- United States
- Language:
- English
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Related Subjects
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-)
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-)