THE DISCRETE GAUSSIAN MODEL, II. INFINITE-VOLUME SCALING LIMIT AT HIGH TEMPERATURE

• 成果类型: Article
• 署名作者: Bauerschmidt, Roland; Park, Jiwoon; Rodriguez, Pierre-Francois
• 署名单位: University of Cambridge; Imperial College London
• 刊物名称: ANNALS OF PROBABILITY
• ISSN/ISSBN: 0091-1798
• DOI: 10.1214/23-AOP1659
• 发表日期: 2024
• 页码: 1360-1398
• 关键词: kosterlitz-thouless transition; renormalization-group analysis; gradient; perturbations; fluctuations; systems

摘要

The Discrete Gaussian model is the lattice Gaussian free field conditioned to be integer-valued. In two dimensions and at sufficiently high temperature, we show that the scaling limit of the infinite-volume gradient Gibbs state with zero mean is a multiple of the Gaussian free field. This article is the second in a series on the Discrete Gaussian model, extending the methods of the first paper by the analysis of general external fields (rather than macroscopic test functions on the torus). As a byproduct, we also obtain a scaling limit for mesoscopic test functions on the torus.