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DY: Fachverband Dynamik und Statistische Physik
DY 26: Critical Phenomena and Phase Transitions
DY 26.5: Vortrag
Mittwoch, 7. September 2022, 11:00–11:15, H20
Population Annealing Monte Carlo Using the Rejection-Free n-Fold Way Update Applied to a Frustrated Ising Model on a Honeycomb Lattice — •Denis Gessert1,2, Martin Weigel1,3, and Wolfhard Janke2 — 1Centre for Fluid and Complex Systems, Coventry University, Coventry, CV1 5FB, United Kingdom — 2Institut für Theoretische Physik, Leipzig University, Postfach 100920, 04009 Leipzig, Germany — 3Institut für Physik, Technische Universität Chemnitz, 09107 Chemnitz, Germany
Population annealing (PA) is a Monte Carlo method well suited for problems with a rough free energy landscape such as glassy systems. PA is similar to repeated simulated annealing, with the addition of a resampling step at each temperature. While a large population may to some extent compensate for imperfect equilibration, it is clear that PA must fail if almost no spins are flipped during equilibration.
This is the case in systems with a phase transition at a very low temperature where a high Metropolis rejection rate makes sampling phase space near infeasible. To overcome this slow-down we propose a combination of the PA framework with the rejection-free “n-fold way” update and achieve an exponential speed-up at low temperatures as compared to Metropolis.
To test our method we study the Ising model with competing ferromagnetic (J1 > 0) nearest and antiferromagnetic (J2 < 0) next-to-nearest neighbor interactions on a honeycomb lattice. As Tc becomes arbitrarily small when approaching the special point J2=−J1/4 with Tc = 0 we consider this a good choice to test the efficacy of our method.