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| -rw-r--r-- | monte-carlo.bib | 17 | ||||
| -rw-r--r-- | monte-carlo.tex | 4 |
2 files changed, 20 insertions, 1 deletions
diff --git a/monte-carlo.bib b/monte-carlo.bib index 0071b74..1ca5ac0 100644 --- a/monte-carlo.bib +++ b/monte-carlo.bib @@ -798,4 +798,21 @@ random field Ising model and finally of quantum spin glasses.}, author = {Kent-Dobias, Jaron}, year = {2018}, note = {https://git.kent-dobias.com/wolff/} +} + +@article{hasenbusch_improved_1990, + title = {Improved estimators for a cluster updating of {O}(n) spin models}, + volume = {333}, + issn = {0550-3213}, + url = {http://www.sciencedirect.com/science/article/pii/055032139090052F}, + doi = {10.1016/0550-3213(90)90052-F}, + abstract = {We present a generalisation of the cluster algorithm introduced by Swendsen and Wang to O(n) spin models. We have found an improved estimator of the susceptibility and the two-point function for this algorithm. Numerical simulations were performed for the XY model and the O(4) model on lattices up to 2562 to check the efficiency of the algorithm and the estimators. We found no indication for critical slowing down.}, + number = {2}, + urldate = {2018-10-20}, + journal = {Nuclear Physics B}, + author = {Hasenbusch, Martin}, + month = mar, + year = {1990}, + pages = {581--592}, + file = {ScienceDirect Full Text PDF:/home/pants/.zotero/data/storage/HMXWXQKA/Hasenbusch - 1990 - Improved estimators for a cluster updating of O(n).pdf:application/pdf;ScienceDirect Snapshot:/home/pants/.zotero/data/storage/FR2HQ3GJ/055032139090052F.html:text/html} }
\ No newline at end of file diff --git a/monte-carlo.tex b/monte-carlo.tex index 3d6ed8e..f5ff8e7 100644 --- a/monte-carlo.tex +++ b/monte-carlo.tex @@ -425,7 +425,9 @@ are preserved, including correlators with the ghost site exists, we expect this representation to extend it to finite field, all other features of the algorithm held constant. For instance, the average cluster size in the Wolff algorithm is often said to be an estimator for the magnetic -susceptibility in the Ising, Potts, and $\mathrm O(n)$ models, but really what +susceptibility in the Ising, Potts, and (with clusters weighted by the +components of their spins along the reflection direction +\cite{hasenbusch_improved_1990}) $\mathrm O(n)$ models, but really what it estimates is the averaged squared magnetization, which corresponds to the susceptibility when the average magnetization is zero. At finite field the latter thing is no longer true, but the correspondence between cluster size |