Nonlocal specific heat

Abstract

The energy-energy correlation function $C\left(k\right)\mathrm{}$ is calculated to $O(4-d)\mathrm{}$ in an exponentiated crossover form for $n$-component spin systems. The result is exact for the Gaussian ($n=2\mathrm{}$) and spherical ($n=\infty$) models which form symmetrically placed anchors for the calculation for general $n$. The error is proprotional to the small critical-point exponent $\eta$ and is likely to be small in three dimensions. A dispersion-theory representation of $C\left(k\right)\mathrm{}$ is used to correct the large-$k$ behavior to the expected Fisher-Langer asymptotic form. The result gives a direct method for the measurement of the correlation length in liquid helium.