Content deleted Content added
added generlizations to frustrated systems |
m Open access bot: hdl added to citation with #oabot. |
||
Line 70:
== Generalizations ==
The algorithm is not efficient in simulating [[Geometrical frustration|frustrated systems]], because the [[Percolation critical exponents|correlation length of the clusters]] is larger than the [[Correlation function (statistical mechanics)|correlation length of the spin model]] in the presence of frustrated interactions.<ref>{{Cite journal|last=Cataudella|first=V.|last2=Franzese|first2=G.|last3=Nicodemi|first3=M.|last4=Scala|first4=A.|last5=Coniglio|first5=A.|date=1994-03-07|title=Critical clusters and efficient dynamics for frustrated spin models|url=https://link.aps.org/doi/10.1103/PhysRevLett.72.1541|journal=Physical Review Letters|volume=72|issue=10|pages=1541–1544|doi=10.1103/PhysRevLett.72.1541|hdl=2445/13250|hdl-access=free}}</ref> Currently, there are two main approaches to addressing this problem, such that the efficiency of cluster algorithms is extended to frustrated systems.
The first approach is to extend the bond-formation rules to more non-local cells, and the second approach is to generate clusters based on more relevant order parameters. In the first case, we have the [[KBD algorithm]] for the [[Domino tiling|fully-frustrated Ising model]], where the decision of opening bonds are made on each plaquette, arranged in a checkerboard pattern on the square lattice.<ref>{{Cite journal|last=Kandel|first=Daniel|last2=Ben-Av|first2=Radel|last3=Domany|first3=Eytan|date=1990-08-20|title=Cluster dynamics for fully frustrated systems|url=https://link.aps.org/doi/10.1103/PhysRevLett.65.941|journal=Physical Review Letters|volume=65|issue=8|pages=941–944|doi=10.1103/PhysRevLett.65.941}}</ref> In the second case, we have [[replica cluster move]] for low-dimensional [[Spin glass|spin glasses]], where the clusters are generated based on spin overlaps, which is believed to be the relevant order parameter.
| |||