Abstract
In cluster tomography, we propose measuring the number of clusters N intersected by a line segment of length ℓ across a finite sample. As expected, the leading order of N(ℓ) scales as aℓ, where a depends on microscopic details of the system. However, at criticality, there is often an additional nonlinearity of the form bln(ℓ), originating from the endpoints of the line segment. By performing large scale Monte Carlo simulations of both two- and three-dimensional percolation, we find that b is universal and depends only on the angles encountered at the endpoints of the line segment intersecting the sample. Our findings are further supported by analytic arguments in two dimensions, building on results in conformal field theory. Being broadly applicable, cluster tomography can be an efficient tool for detecting phase transitions and characterizing the corresponding universality class in classical or quantum systems with a relevant cluster structure.
| Original language | English (US) |
|---|---|
| Article number | 043218 |
| Journal | Physical Review Research |
| Volume | 5 |
| Issue number | 4 |
| DOIs | |
| State | Published - Oct 2023 |
Funding
We thank W. Witczak-Krempa for helpful discussions. We would like to acknowledge the WCAS Summer Grant Award from the Weinberg College Baker Program in Undergraduate Research at Northwestern University. This work was supported by the National Science Foundation under Grant No. PHY-2310706 of the QIS program in the Division of Physics. This research was supported in part through the computational resources and staff contributions provided for the Quest high performance computing facility at Northwestern University which is jointly supported by the Office of the Provost, the Office for Research, and Northwestern University Information Technology.
ASJC Scopus subject areas
- General Physics and Astronomy