The Scaling Limit of the (∇ + Δ) -Model

Authors

Alessandra Cipriani, Delft University of Technology
Biltu Dan, Indian Statistical Institute, Kolkata
Rajat Subhra Hazra, Indian Statistical Institute, Kolkata

Article Type

Research Article

Publication Title

Journal of Statistical Physics

Abstract

In this article we study the scaling limit of the interface model on Zd where the Hamiltonian is given by a mixed gradient and Laplacian interaction. We show that in any dimension the scaling limit is given by the Gaussian free field. We discuss the appropriate spaces in which the convergence takes place. While in infinite volume the proof is based on Fourier analytic methods, in finite volume we rely on some discrete PDE techniques involving finite-difference approximation of elliptic boundary value problems.

DOI

10.1007/s10955-021-02717-1

Publication Date

2-1-2021

Comments

Open Access, Green

Recommended Citation

Cipriani, Alessandra; Dan, Biltu; and Hazra, Rajat Subhra, "The Scaling Limit of the (∇ + Δ) -Model" (2021). Journal Articles. 2100.
https://digitalcommons.isical.ac.in/journal-articles/2100