Journal of Statistical Physics ( IF 1.243 ) Pub Date : 2020-05-20 , DOI: 10.1007/s10955-020-02560-w
Federico Camia, Jianping Jiang, Charles M. Newman

Let $$\Phi ^h(x)$$ with $$x=(t,y)$$ denote the near-critical scaling limit of the planar Ising magnetization field. We take the limit of $$\Phi ^h$$ as the spatial coordinate y scales to infinity with t fixed and prove that it is a stationary Gaussian process X(t) whose covariance function K(t) is the Laplace transform of a mass spectral measure $$\rho$$ of the relativistic quantum field theory associated to the Euclidean field $$\Phi ^h.$$X and K should provide a useful tool for studying the mass spectrum; e.g., the small distance/time behavior of the covariance functions of $$\Phi ^h$$ and X(t) shows that $$\rho$$ is finite but has infinite first moment.

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