# Limits of 3D Ising and Solid-On-Solid Interfaces

> **NSF 01002526DB NSF RESEARCH & RELATED ACTIVIT** · New York University (NY) · $240,000

## Abstract

This project aims to study a variety of problems addressing fundamental features of the classical three-dimensional Ising model and its (2+1)-dimensional Solid-On-Solid (SOS) approximation at low temperature, which are central to understanding crystal growth and formation. The main focus will be on longstanding conjectures concerning the fluctuations of these surfaces and the scaling limits of the models when positioned on a slope and on a hard wall. This project also provides research opportunities for graduate students. 

The first research direction concerns the 3D Ising model and its (2+1)D SOS approximation at low temperature, with boundary conditions that force these random surfaces to have a positive slope. It is widely believed that, above a slope, the low temperature rigidity of these surfaces will destabilize, and their scaling limits should be a Gaussian Free Field (GFF). Little progress has been made on this problem until a recent successful study of a variant of the SOS model. The project outlines a program building on this recent progress, aiming to establish a GFF limit for the true SOS model and, thereafter, 3D Ising. The second research direction focuses on the 3D Ising and (2+1)D SOS surfaces above a hard flat wall. The plan is to solve key questions, addressing the typical height and shape of the Ising surface in that setting, and the fluctuations of the SOS level lines. The third research direction aims to study the SOS model above a hard wall (as above)

## Key facts

- **NSF award ID:** 2451083
- **Awardee organization:** New York University (NY)
- **SAM.gov UEI:** NX9PXMKW5KW8
- **PI:** Eyal Lubetzky
- **Primary program:** 01002526DB NSF RESEARCH & RELATED ACTIVIT
- **All programs:** —
- **Estimated total:** $240,000
- **Funds obligated:** $240,000
- **Transaction type:** Standard Grant
- **Period:** 07/01/2025 → 06/30/2027

## Primary source

NSF Award Search: https://www.nsf.gov/awardsearch/showAward?AWD_ID=2451083

## Citation

> US National Science Foundation, Award 2451083, Limits of 3D Ising and Solid-On-Solid Interfaces. Retrieved via AI Analytics 2026-06-07 from https://api.ai-analytics.org/grant/nsf/2451083. Licensed CC0.

---

*[NSF Awards dataset](/datasets/nsf-awards) · CC0 1.0*