• Corpus ID: 119151230

The dynamical sine-Gordon model in the full subcritical regime

  title={The dynamical sine-Gordon model in the full subcritical regime},
  author={A. Ramesh Chandra and Martin Hairer and Hao Shen},
  journal={arXiv: Probability},
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… 
A novel probabilistic approach to renormalization of the two-dimensional boundary (or 1-dimensional) Sine-Gordon model up to the KT threshold β = √ 2 is presented and a refinement of classical electrostatic inequalities is proved, which allows to bound the energy of configurations in terms of the Wasserstein distance between + and − charges.
Hopf and pre-Lie algebras in regularity structures
These lecture notes aim to present the algebraic theory of regularity structures as developed in [Hai14, BHZ19, BCCH21]. The main aim of this theory is to build a systematic approach to
Smoluchowski-Kramers approximation for the singular stochastic wave equations in two dimensions
We study a family of nonlinear damped wave equations indexed by a parameter ε > 0 and forced by a space-time white noise on the two dimensional torus, with polynomial and sine nonlinearities. We show
Local operators in the Sine-Gordon model: ∂ µ φ ∂ ν φ and the stress tensor
: We consider the simplest non-trivial local composite operators in the massless Sine-Gordon model, which are ∂ µ φ ∂ ν φ and the stress tensor T µν . We show that even in the finite regime β 2 < 4 π
The microlocal irregularity of Gaussian noise
The study of random Fourier series, linear combinations of trigonometric functions whose coefficients are independent (in our case Gaussian) random variables with polynomially bounded means and
Maximum and coupling of the sine-Gordon field
For $0<\beta<6\pi$, we prove that the distribution of the centred maximum of the $\epsilon$-regularised continuum sine-Gordon field on the two-dimensional torus converges to a randomly shifted Gumbel
Stochastic quantization associated with the $$\exp (\Phi )_2$$-quantum field model driven by space-time white noise on the torus in the full $$L^1$$-regime
The present paper is a continuation of our previous work (Hoshino et al., J Evol Equ 21:339–375, 2021) on the stochastic quantization of the $$\exp (\Phi )_2$$ exp ( Φ ) 2 -quantum
Resonance-based schemes for dispersive equations via decorated trees
Abstract We introduce a numerical framework for dispersive equations embedding their underlying resonance structure into the discretisation. This will allow us to resolve the nonlinear oscillations
Study of a fractional stochastic heat equation
Abstract. In this article, we study a d-dimensional stochastic nonlinear heat equation (SNLH) with a quadratic nonlinearity, forced by a fractional space-time white noise: { ∂tu− ∆u = ρ2u2 + Ḃ , t ∈
Renormalising singular stochastic PDEs without extended decorations
Extended decorations on naturally decorated trees were introduced in the work of Bruned, Hairer and Zambotti on algebraic renormalization of regularity structures to provide a convenient framework


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
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
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.