Tunneling times and density of states in multicanonical simulation methods

Ying Wai Li, Alfred C.K. Farris, Markus Eisenbach

David M. Ceperley

Bernd A. Berg, Thomas Neuhaus

Relying on the recent proposed multicanonical algorithm, we present a numerical simulation of the first-order phase transition in the 2D 10-state Potts model on lattices up to sizes 100\ifmmode\times\else\texttimes\fi{}100. It is demonstrated that the new algorithm lacks an exponentially fast increase of the tunneling time between metastable states as a function of the linear size L of the system. Instead, the tunneling time diverges approximately proportional to ${\mathit{L}}^{2.65}$. On our largest lattice we gain more than 2 orders of magnitude as compared to a standard heat-bath algorithm. As a first physical application we report a high-precision computation of the interfacial free energy per unit area.

Simon Trebst

We determine the optimal scaling of local‐update flat‐histogram methods (such as multicanonical, broad histograms, tempering, or Wang‐Landau sampling) with system size by using a perfect flat‐histogram scheme based on the exact density of states of 2D Ising models. We find that the Wang‐Landau algorithm shows the same scaling as the perfect scheme and is thus optimal. However, even for the perfect scheme the scaling with the number of spins N is slower than the minimal N2 of an unbiased random walk in energy space for both, local and N‐fold way updates. While it still follows a power law N2Lz for the ferromagnetic and fully frustrated Ising model we find exponential scaling of the tunneling times in the case of the ±J Ising spin glass. The tunneling times of the ±J Ising spin glass are found to follow a fat‐tailed Fréchet extremal value distribution.

Zvi Kotler, Abraham Nitzan, Ronnie Kosloff

Bernd A. Berg, T. Çelik, Ulrich H. E. Hansmann

We simulated the Edwards-Anderson Ising spin glass model in three dimensions via the recently proposed multicanonical ensemble. Physical quantities such as energy density, specific heat and entropy are evaluated at all temperatures. We studied their finite-size scaling, as well as the zero-temperature limit to explore the ground-state properties. Our estimate of the ground-state entropy per spin is s 0 = 0.046 ÷ 0.002.