Gaussian fluctuations for the classical XY model

2016/05/04 by Newman, Charles M., Wu, Wei · 2 citations
#60F05 #60G60 #82B20 #FOS: Mathematics #FOS: Physical sciences #Mathematical Physics (math-ph) #Probability (math.PR)

paper · doi:10.48550/arxiv.1605.01297

Abstract

We study the classical XY model in bounded domains of ℤ^d with Dirichlet boundary conditions. We prove that when the temperature goes to zero faster than a certain rate as the lattice spacing goes to zero, the fluctuation field converges to a standard Gaussian white noise. This and related results also apply to a large class of gradient field models.

Cited by

• Central limit theorems for non-linear functionals of Gaussian fields via Wiener chaos decomposition
• Scaling limit of the discrete Gaussian free field with degenerate random conductances

Related

• Temperature-dependent fluctuations in the two-dimensionalXYmodel
• Fluctuations of a nonlinear stochastic heat equation in dimensions three and higher
• Space-time fluctuation of the Kardar-Parisi-Zhang equation in d≥ 3 and the Gaussian free field
• Gaussian fluctuation for spatial average of parabolic Anderson model with Neumann/Dirichlet/periodic boundary conditions
• Gaussian beta ensembles at high temperature: eigenvalue fluctuations and bulk statistics