Arttu Rajantie, Kari Rummukainen, David J. Weir
In the Yang-Mills theory, the apparent thickness of the confining string is known to grow logarithmically when its length increases. The same logarithmic broadening also happens to strings in other quantum field theories and domain walls in statistical physics models. Even in quantum field theories, the observables used to measure and characterise this phenomenon are largely borrowed from statistical physics. In this paper, we describe it using the string form factor, which is a meaningful quantum observable, and show how the form factor can be obtained from field correlation functions calculated in lattice Monte Carlo simulations. We apply this method to 2+1-dimensional scalar theory in the strong coupling limit, where it is equivalent to the 3D Ising model, and through duality also to 2+1-dimensional $\mathbb{Z}_2$ gauge theory. We measure the string form factor by simulating the Ising model, and demonstrate that it displays the same logarithmic broadening as statistical physics observables.
View original:
http://arxiv.org/abs/1210.1106
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