• Corpus ID: 119151230

The dynamical sine-Gordon model in the full subcritical regime

@article{Chandra2018TheDS,
  title={The dynamical sine-Gordon model in the full subcritical regime},
  author={A. Ramesh Chandra and Martin Hairer and Hao Shen},
  journal={arXiv: Probability},
  year={2018}
}
We prove that the dynamical sine-Gordon equation on the two dimensional torus introduced in [HS16] is locally well-posed for the entire subcritical regime. At first glance this equation is far out of the scope of the local existence theory available in the framework of regularity structures [Hai14, BHZ16, CH16, BCCH17] since it involves a non-polynomial nonlinearity and the solution is expected to be a distribution (without any additional small parameter as in [FG17, HX18]). In [HS16] this was… 
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References

SHOWING 1-10 OF 21 REFERENCES
The Dynamical Sine-Gordon Model
We introduce the dynamical sine-Gordon equation in two space dimensions with parameter $${\beta}$$β, which is the natural dynamic associated to the usual quantum sine-Gordon model. It is shown that
DESTRUCTION OF LONG-RANGE ORDER IN ONE-DIMENSIONAL AND TWO-DIMENSIONAL SYSTEMS POSSESSING A CONTINUOUS SYMMETRY GROUP . II . QUANTUM
The asymptotic behavior of the correlations in the low-temperature phase are found for the following two-dimensional quantum systems: a two-dimensional lattice of plane rotators, two-dimensional
A Course on Rough Paths
We give a short overview of the scopes of both the theory of rough paths and the theory of regularity structures. The main ideas are introduced and we point out some analogies with other branches of
Critical dynamics of the sine-Gordon model ind=2−ε dimensions
AbstractThe renormalization scheme of Amit, Goldschmidt and Grinstein is extended tod=2−ε dimensions. The exponent ν of the correlation lengthv−1=2ε+O(ε2) is in agreement with the result of
Classical and quantum statistical mechanics in one and two dimensions: Two-component Yukawa — and Coulomb systems
We estimate the canonical and grand canonical partition function in a finite volume and prove stability and existence of the thermodynamic limit for the pressure of two component classical and
Large scale limit of interface fluctuation models
We extend the weak universality of KPZ in [Hairer-Quastel] to weakly asymmetric interface models with general growth mechanisms beyond polynomials. A key new ingredient is a pointwise bound on
Dynamical Liouville
  • C. Garban
  • Computer Science
    Journal of Functional Analysis
  • 2020
Dynamics of the orientational roughening transition.
  • Kahng, Park
  • Physics
    Physical review. B, Condensed matter
  • 1993
We use the renormalization-group method to study the dynamics of the sine-Gordon model for the orientational roughening transition. Implications of our results for spatial and temporal behavior of
Renormalisation of parabolic stochastic PDEs
TLDR
It transpires that some of these universal objects are described by singular stochastic PDEs, and a survey of the recently developed theory of regularity structures which allows to build these objects and to describe some of their properties is given.
...
...