Dresden 2014 – wissenschaftliches Programm
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DY: Fachverband Dynamik und Statistische Physik
DY 8: Critical Phenomena and Phase Transitions
DY 8.10: Vortrag
Montag, 31. März 2014, 17:45–18:00, ZEU 118
Universal shape functions at classical critical points — •Stephen Inglis1, Jean-Marie Stèphan2, Paul Fendley2, and Roger G. Melko1,3 — 1University of Waterloo, Waterloo, Canada — 2University of Virginia, Charlottesville, USA — 3Perimeter Institute for Theoretical Physics, Waterloo, Canada
We demonstrate how the Rènyi mutual information (RMI) can be used to characterize universality at the critical point of two dimensional classical systems through their shape dependence, similar to the result of c-theorems in one dimensional systems.
We introduce a highly efficient method for calculating the RMI in discrete classical systems, and use it on the two dimensional Ising and Potts models. This method avoid the difficulty of thermodynamic integration needed in earlier techniques [Phys. Rev. B 87, 195134 (2013)] and allows for direct access to the RMI for different geometries. The method is similar to the quantum ratio trick [Phys. Rev. Lett. 104, 157201 (2010)] except that we gain a large increase in speed and convergence by using classical Monte Carlo. In the cases where classical critical points contain the universality class of interest, this method represents a more efficient approach for extracting universal shape functions.