A six-loop field-theoretic calculation gives the fractal dimension of critical curves and the crossover exponent in O(n) models, with estimates for LERW, SAW, Ising, XY and Heisenberg systems.
Critical curves in conformally invariant statistical systems
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abstract
We consider critical curves -- conformally invariant curves that appear at critical points of two-dimensional statistical mechanical systems. We show how to describe these curves in terms of the Coulomb gas formalism of conformal field theory (CFT). We also provide links between this description and the stochastic (Schramm-) Loewner evolution (SLE). The connection appears in the long-time limit of stochastic evolution of various SLE observables related to CFT primary fields. We show how the multifractal spectrum of harmonic measure and other fractal characteristics of critical curves can be obtained.
fields
cond-mat.stat-mech 1years
2019 1verdicts
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Fractal dimension of critical curves in the $O(n)$-symmetric $\phi^4$-model and crossover exponent at 6-loop order: Loop-erased random walks, self-avoiding walks, Ising, XY and Heisenberg models
A six-loop field-theoretic calculation gives the fractal dimension of critical curves and the crossover exponent in O(n) models, with estimates for LERW, SAW, Ising, XY and Heisenberg systems.