Verdier-Stockmayer algorithm

Fig. 1.4 Various examples of dynamic Monte Carlo algorithms for SAWs sites taken by beads are shown by dots, and bonds connecting the bead are shown by lines. Bonds that are moved are shown as a wavy line (before the move) or broken line (after the move), while bonds that are not moved are shown as full lines, (a) Generalized Verdier-Stockmayer algorithm on the simple cubic lattice showing three type of motions end-bond motion, kink-jump motion, 90° crankshaft rotation (b) slithering snake algorithm (c) pivot algorithm. (From Kremer and Binder )...

This nonergodicity is in fact quite easy to see consider the double cul-de-sac configuration shown in Fig. 2.10(a). This SAW is completely frozen under elementary moves A, B, D and F it cannot transform itself into any other state, nor can it be reached from any other state. It follows that the original Verdier-Stockmayer algorithm and most of its generaliza-tions are nonergodic (in d=l) already for 11. 

Fig. 2.10 Some double cul-de-sac configurations, frozen in the Verdier-Stockmayer algorithm and its generalizations.

The nonergodicity of the Verdier-Stockmayer algorithm due to double culs-de-sac was noticed already by Verdier in 1969. 

The Verdier-Stockmayer (pure one-bead) and Kranbuehl-Verdier (pure two-bead) algorithms for the SAW or NRRW (but not the ORW) have peculiar conservation laws which inhibit the relaxation of the chain, thereby... 

Historically the earliest dynamic Monte Carlo algorithms for the SAW were local A-conserving algorithms they date back to the work of Delbriick"" and Verdier and Stockmayer , both published in 1962. During the subsequent two decades, mnnerous variants on this theme were proposed (see Table 2.4). Most of these algorithms employ some subset of moves A-F from Figs 2.1 and 2.2. 

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