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 autocorrelation time, as well as the finite size scaling of the “thickness” observable used in an earlier lattice study by Hasenbusch et al.
Highlights
We obtain nonperturbative results on the sine-Gordon model using the lattice field technique
Many revolutions in theoretical physics occured in the early 1970s; one of these was the discovery that phase transitions did not always associate themselves with spontaneous symmetry breaking and long-range order
The physics of vortices, and the corresponding topological phase transitions, allowed one to avoid the theorems that opposed spontaneous symmetry breaking in two dimensions
Summary
We describe the Fourier accelerated hybrid Monte Carlo (HMC) algorithm that is used in our simulations [9, 10]. The HMC simulation proceeds as usual; the momentum field π(x) is drawn at random from a Gaussian distribution with unit variance This corresponds to “integrating in” a Gaussian field in the partition function, leading to the “Hamilitonian”. The Fourier acceleration enters into the leapfrog trajectory, where the Fourier modes of φ(x) and π(x) are integrated with a step size dt(k) = dt/(∆(k) + m2eff). The present study is partly a preliminary step to this more extensive analysis of Fourier acceleration, using the sine-Gordon model as a working context. This is partly motivated by the fact that two-dimensional real scalar field theories are simulated on relatively small scale computing resources, and are well-suited to exploratory studies
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