The ideas behind the Self Consistent Expansion

Abstract

In recent years we have witnessed a growing interest in various non-equilibrium systems described in terms of stochastic non-linear field theories. In some of those systems like the KPZ and related models, the interesting behavior is in the strong coupling regime, which is inaccessible by traditional perturbative treatments such as dynamical renormalization group (DRG). A useful tool in the study of such system is the Self Consistent Expansion (SCE), which might be said to generate its own "small parameter" .The self consistent expansion (SCE) has the advantage that its structure is just that of a regular expansion, the only difference is that the simple system around which the expansion is performed is adjustable. The purpose of the this article is to present the method in a simple and understandable way, that hopefully will make it accessible to a wider public working on non-equilibrium statistical physics.

17 pages, 3 figures. Submitted to a focus issue of JSTAT on Disorder, Fluctuations and Universality dedicated to Thomas Nattermann

References in corpus (13)

• Anomalous roughening of wood fractured surfaces
• On the Perturbation Expansion of the KPZ-Equation
• Nonlocality in kinetic roughening
• Roughening Transition in a Moving Contact Line
• The Kardar-Parisi-Zhang Equation with Temporally Correlated Noise - A Self Consistent Approach
• Numerical Evidence for Stretched Exponential Relaxations in the Kardar-Parisi-Zhang Equation
• New Results for the Nonlocal Kardar-Parisi-Zhang Equation
• Self Consistent Expansion for the Molecular Beam Epitaxy Equation
• Existence of the upper critical dimension of the Kardar-Parisi-Zhang equation
• Roughness of tensile crack fronts in heterogenous materials
• Roughness of moving elastic lines - crack and wetting fronts
• Streched exponential in non-linear stochastic filed theories
• Vortex lines in the three-dimensional XY model with random phase shifts

Cited by in corpus (13)

• Nonperturbative renormalization group for the stationary Kardar-Parisi-Zhang equation: scaling functions and amplitude ratios in 1+1, 2+1 and 3+1 dimensions
• Nonequilibrium fluctuations of an interface under shear
• Anomalous scaling at non-thermal fixed points of Burgers' and Gross-Pitaevskii turbulence
• Random Close Packing and the Hard Sphere Percus-Yevick Theory
• Strong anisotropy in two-dimensional surfaces with generic scale invariance: Gaussian and related models
• Inferring entropy from structure
• A Deal with the Devil: From Divergent Perturbation Theory to an Exponentially-Convergent Self-Consistent Expansion
• Addressing energy density functionals in the language of path-integrals I: Comparative study of diagrammatic techniques applied to the (0+0)-D $O(N)$-symmetric ${\phi }^4$-theory
• The Structure of Fluctuating Thin Sheets Under Random Forcing
• Power countings versus physical scalings in disordered elastic systems - Case study of the one-dimensional interface
• Dynamics of Fluctuating Thin Sheets Under Random Forcing
• Thermally driven elastic membranes are quasi-linear across all scales
• Asymptotic Matching the Self-Consistent Expansion to Approximate the Modified Bessel Functions of the Second Kind