Euclidean Dynamical Triangulation revisited: is the phase transition really first order?

TL;DR

This study revisits the phase transition in 4D Euclidean Dynamical Triangulation, employing improved numerical methods to confirm that the transition is indeed first order, contrary to earlier beliefs of second order.

Contribution

The paper introduces enhanced simulation techniques that address previous methodological issues, conclusively demonstrating the first order nature of the phase transition in 4D Euclidean Dynamical Triangulation.

Findings

Confirmed the first order phase transition with larger system sizes

Improved numerical methods reduced systematic errors

Demonstrated the robustness of the first order transition conclusion

Abstract

The transition between the two phases of 4D Euclidean Dynamical Triangulation [1] was long believed to be of second order until in 1996 first order behavior was found for sufficiently large systems [3,4]. However, one may wonder if this finding was affected by the numerical methods used: to control volume fluctuations, in both studies [3,4] an artificial harmonic potential was added to the action; in [4] measurements were taken after a fixed number of accepted instead of attempted moves which introduces an additional error. Finally the simulations suffer from strong critical slowing down which may have been underestimated. In the present work, we address the above weaknesses: we allow the volume to fluctuate freely within a fixed interval; we take measurements after a fixed number of attempted moves; and we overcome critical slowing down by using an optimized parallel tempering algorithm [6]. With these improved methods, on systems of size up to 64k 4-simplices, we confirm that the phase transition is first order.