Large scale behaviour of 3D continuous phase coexistence models

Abstract

We study a class of three dimensional continuous phase coexistence models, and show that, under different symmetry assumptions on the potential, the large-scale behaviour of such models near a bifurcation point is described by the dynamical ${\Phi }_3^p$ models for $p\in \{2,3,4\}$. This result is specific to space dimension $3$ and does not hold in dimension $2$.

54 pages. Added proof for global in time convergence

References in corpus (3)

• A central limit theorem for the KPZ equation
• Singular stochastic PDEs
• The Hairer--Quastel universality result in equilibrium

Cited by in corpus (11)

• Renormalising SPDEs in regularity structures
• A variational method for ${\Phi }_3^4$
• Discretisation of regularity structures
• Weak universality for a class of 3d stochastic reaction-diffusion models
• Weak universality of dynamical ${\Phi }_3^4$: non-Gaussian noise
• Paracontrolled quasilinear SPDEs
• Large-scale limit of interface fluctuation models
• Glauber dynamics of 2D Kac-Blume-Capel model and their stochastic PDE limits
• Weak universality of the dynamical ${\Phi }_3^4$ model on the whole space
• Moment bounds for SPDEs with non-Gaussian fields and application to the Wong-Zakai problem
• Sharp convergence of nonlinear functionals of a class of Gaussian random fields