Sampling of General Correlators in Worm Algorithm-based Simulations

Abstract

Using the complex ${\varphi }^4$-model as a prototype for a system which is simulated by a worm algorithm, we show that not only the charged correlator $<{\varphi }^{\ast }(x)\varphi (y)>$, but also more general correlators such as $<|\varphi (x)||\varphi (y)|>$ or $<\text{arg}(\varphi (x))\text{arg}(\varphi (y))>$, as well as condensates like $<|\varphi |>$, can be measured at every step of the Monte Carlo evolution of the worm instead of on closed-worm configurations only. The method generalizes straightforwardly to other systems simulated by worms, such as spin or sigma models.

Comments: 43 pages, 15 figures