Dynamic sine-Gordon renormalization of the Laplacian roughening transition below two dimensions

Park, K.; Kahng, B.

doi:10.1103/physrevb.49.7026

Cited by 2 publications

(1 citation statement)

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“…The critical value β 2 = 8π can be interpreted as the critical inverse temperature at which total collapse takes place, giving rise to a Kosterlitz-Thouless phase transition [KT73,FS81]. Finally, the model (1.1) has also been proposed as a model for the dynamic of crystalvapour interfaces at the roughening transition [CW78,Neu83] and as a model of crystal surface fluctuations in equilibrium [KP93,KP94].…”

Section: Introductionmentioning

confidence: 99%

The Dynamical Sine-Gordon Model

Hairer

Shen

2015

Commun. Math. Phys.

150

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We introduce the dynamical sine-Gordon equation in two space dimensions with parameter β, which is the natural dynamic associated to the usual quantum sineGordon model. It is shown that when β 2 ∈ (0, 16π 3 ) the Wick renormalised equation is well-posed. In the regime β 2 ∈ (0, 4π), the Da Prato-Debussche method [DPD02, DPD03] applies, while for3 ), the solution theory is provided via the theory of regularity structures [Hai13]. We also show that this model arises naturally from a class of 2+1-dimensional equilibrium interface fluctuation models with periodic nonlinearities.The main mathematical difficulty arises in the construction of the model for the associated regularity structure where the role of the noise is played by a non-Gaussian random distribution similar to the complex multiplicative Gaussian chaos recently analysed in [LRV13].

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