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DY: Fachverband Dynamik und Statistische Physik
DY 15: Focus Session: Large Deviations and Rare Events II
DY 15.3: Talk
Monday, March 9, 2026, 15:45–16:00, ZEU/0114
Large deviation simulation of the coupling time of an Ising ferromagnet — •Mathis Groenhagen1, Peter Werner2, and Alexander K. Hartmann1 — 1Institut für Physik, Carl von Ossietzky Universität Oldenburg — 2Laboratoire de Météorologie Dynamique - ENS, Paris
Coupling from the past, introduced by Propp and Wilson [1], is a Markov-chain Monte Carlo (MCMC) method capable of generating perfectly independent samples from a finite set of states, following exactly a given distribution. The performance of this algorithm for a given model can be characterized by it’s coupling time τc, which measures the time to perfect statistical independence and depends on the used random numbers.
The algorithm is tested for one and two-dimensional Ising models without external field with the single-spin-update heat-bath algorithm. In order to access the distribution p(τc) over a wide range of the support down to densities as small as 10−200, a large-deviation MCMC algorithm is used. With this, we have obtained p(τc) for different lattice dimensions D, edge lengths L and heat-bath temperatures T.
In particular, we observe a change of the shape of p(τc) at Tc for D=2. For the paramagnetic case of D=2 and D=1, p(τc) follows a Gumbel distribution as predicted for the thermodynamic limit [2]. We have studied the dependency of the distribution parameters on T and L.
[1] J. Propp, D. Willson, Random Struct. Algoritms 9, 223-252 (1996).
[2] A. Collevechio et al., J. Stat. Phys. 170, 22-61 (2018).
Keywords: computer simulations; large deviation theory; Ising model; ferromagnet; coupling from the past