Abstract
We obtain nonperturbative results on the sine-Gordon model using the lattice field technique. In particular, we employ the Fourier accelerated hybrid Monte Carlo algorithm for our studies. We find the critical temperature of the theory based on autocorrelation time, as well as the finite size scaling of the "thickness" observable used in an earlier lattice study by Hasenbusch et al. We study the entropy, which is smooth across all temperatures, supportive of an infinite order transition. This system has a well-known duality with the massive Thirring model, which can play the role of a toy models for Montonen-Olive duality in N=4 super-Yang-Mills theory, since it relates solitons to elementary field excitations. Our research lays a groundwork for such study on the lattice.
Highlights
There were many important advances in theoretical physics in the early 1970s. Among these was the discovery of phase transitions that were not characterized by spontaneous symmetry breaking and long-range order
The dynamics of vortices, and the corresponding topological phase transitions, provided a way to have critical phenomena while still satisfying the theorems forbidding spontaneous symmetry breaking in two dimensions
III we review the relation between the 2d Coulomb gas and the sine-Gordon model, which allows us to exhibit the fugacity expansion
Summary
There were many important advances in theoretical physics in the early 1970s. Among these was the discovery of phase transitions that were not characterized by spontaneous symmetry breaking and long-range order. One interesting feature of the XY model is that there is a line of conformal fixed points, rather than a single temperature at which the theory is critical Throughout this low temperature regime there is algebraic ordering of the Oð2Þ spin fields; i.e., correlation functions yield power laws of the separation between operators. The sine-Gordon model belongs to the family of solidon-solid (SOS) models which have critical behavior consistent with the BKT transition. It was mentioned above that the sine-Gordon theory is a toy model for N 1⁄4 4 super-Yang Mills theory because it has a line of fixed points where nontrivial conformal field theories exist. The appendixes discuss some of the technical points of our implementation, and general musings about the fugacity expansion
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