Abstract
We study the classical XY model in bounded domains of Zd 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 Gaussian white noise. This and related results also apply to a large class of gradient field models.
Original language | English (US) |
---|---|
Pages (from-to) | 1759-1777 |
Number of pages | 19 |
Journal | Annales de l'institut Henri Poincare (B) Probability and Statistics |
Volume | 54 |
Issue number | 4 |
DOIs | |
State | Published - Nov 2018 |
Keywords
- Central limit theorem
- Gaussian free field
- Gradient field models
- Random walk representation
- Spin-wave approximation
- XY model
ASJC Scopus subject areas
- Statistics and Probability
- Statistics, Probability and Uncertainty