Nonflat histogram techniques for spin glasses

Abstract

We study the bimodal Edwards-Anderson spin glass comparing established methods, namely the multicanonical method, the 1/k-ensemble and parallel tempering, to an approach where the ensemble is modified by simulating power-law-shaped histograms in energy instead of flat histograms as in the standard multicanonical case. We show that by this modification a significant speed-up in terms of mean round-trip times can be achieved for all lattice sizes taken into consideration.

Wang-Landau simulations with non-flat distributions

“…Due to their rough energy landscape spin-glass systems pose an interesting challenge and serve as benchmark cases for Monte Carlo methods. In a recent study [8] it has been demonstrated that for equilibrium (f = 1) simulations a power-law profile with a strong emphasis of…”

“…which is based on the profile that was used for N ≤ 8 3 in [8]. In the beginning f = e and the simulation is stopped if f < exp 10 −8 .…”

“…It is also understood [6,7] that the multicanonical method can be improved if one aims at a distribution in energy that is proportional to a non-trivial profile instead of constant. Recently we have shown how simulations of spin glasses can be improved when a specially designed profile is used [8]. However, when it comes to the closely related and widely applied Wang-Landau method [9] changing to a profile is not as straightforward as for the other methods and we are not aware of any application of such a modified Wang-Landau method.…”

Monte Carlo Simulation of Long Hard‐Sphere Polymer Chains in Two to Five Dimensions

“…A benchmark comparison for the B1 domain of protein G is in preparation. [24] We also introduced a nonflat histogram technique [25] that generalizes the commonly employed flat multicanonical method [26][27][28] and later adapted this idea also to Wang-Landau simulations [28,29] with nonflat distributions. [30] While in Ref.…”

Monte Carlo Simulation of Long Hard-Sphere Polymer Chains in Two to Five Dimensions

“…While in Ref. [25] we first drew connection to recent work [31] and exemplified the method in a ground-state study for the Edwards-Anderson spin-glass model, in the latter paper [30] we explicitly demonstrated the usefulness of the proposed method for unraveling the intriguing low-temperature "crystal-like" patterns of Lennard-Jones polymers. Currently we are employing this method for determining the ground-state patterns of lattice peptides described by the HP model [32].…”