The Gaussian process for particle masses in the near-critical Ising model

Abstract

We review the construction of a stationary Gaussian process $X(t)$ starting from the near-critical continuum scaling limit ${\Phi }^h$ of the Ising magnetization and its relation to the mass spectrum of the relativistic quantum field theory associated to ${\Phi }^h$. Then for the near-critical Ising model on $a{\mathbb{Z}}^2$ with external field $a^{15/8}h$, we study the renormalized magnetization along a vertical line (with horizontal coordinate approximately $t$) and prove that the limit as $a\downarrow 0$ is the same Gaussian process $X(t)$. We also explore the possible extension of this approach to dimensions $d>2$.

15 pages

References in corpus (2)

• The importance of the Ising model
• Conformal Measure Ensembles and Planar Ising Magnetization: A Review