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diff --git a/monte-carlo.bib b/monte-carlo.bib index 58234c4..4d8669e 100644 --- a/monte-carlo.bib +++ b/monte-carlo.bib @@ -528,3 +528,28 @@ random field Ising model and finally of quantum spin glasses.}, pages = {295--341}, file = {arXiv\:cond-mat/9411017 PDF:/home/pants/.zotero/data/storage/NTUDS8GH/Rieger - 1995 - Monte Carlo Studies of Ising Spin Glasses and Rand.pdf:application/pdf} } + +@article{mermin_topological_1979, + title = {The topological theory of defects in ordered media}, + volume = {51}, + url = {https://link.aps.org/doi/10.1103/RevModPhys.51.591}, + doi = {10.1103/RevModPhys.51.591}, + abstract = {Aspects of the theory of homotopy groups are described in a mathematical style closer to that of condensed matter physics than that of topology. The aim is to make more readily accessible to physicists the recent applications of homotopy theory to the study of defects in ordered media. Although many physical examples are woven into the development of the subject, the focus is on mathematical pedagogy rather than on a systematic review of applications.}, + number = {3}, + urldate = {2018-05-09}, + journal = {Reviews of Modern Physics}, + author = {Mermin, N. D.}, + month = jul, + year = {1979}, + pages = {591--648}, + file = {APS Snapshot:/home/pants/.zotero/data/storage/GD9PHBAV/RevModPhys.51.html:text/html;Mermin - 1979 - The topological theory of defects in ordered media.pdf:/home/pants/.zotero/data/storage/ZJE9JPN6/Mermin - 1979 - The topological theory of defects in ordered media.pdf:application/pdf} +} + +@misc{bierbaum_ising.js_nodate, + title = {ising.js}, + url = {https://mattbierbaum.github.io/ising.js/}, + urldate = {2018-05-15}, + author = {Bierbaum, Matthew K.}, + note = {Source: https://github.com/mattbierbaum/ising.js}, + file = {ising.js:/home/pants/.zotero/data/storage/XR534SY3/ising.html:text/html} +} diff --git a/monte-carlo.pdf b/monte-carlo.pdf Binary files differindex f8e5eea..00f87c8 100644 --- a/monte-carlo.pdf +++ b/monte-carlo.pdf diff --git a/monte-carlo.tex b/monte-carlo.tex index a305aa8..222d6ed 100644 --- a/monte-carlo.tex +++ b/monte-carlo.tex @@ -395,7 +395,10 @@ Since the symmetry group and the spins are described by the same elements, performing the algorithm on the Ising model in a field is fully described by just using the `ghost spin' representation. This algorithm or algorithms based on the same decomposition of the Hamiltonian have been applied -by several researchers \cite{alexandrowicz_swendsen-wang_1989, wang_clusters_1989, ray_metastability_1990}. +by several researchers \cite{alexandrowicz_swendsen-wang_1989, +wang_clusters_1989, ray_metastability_1990}. The algorithm has been +implemented by one of the authors in an existing interactive Ising +simulator at \texttt{https://mattbierbaum.github.io/ising.js} \cite{bierbaum_ising.js_nodate}. \emph{The $\mathrm O(n)$ model.} In the $\mathrm O(n)$ model spins are described by vectors on the $(n-1)$-sphere $S^{n-1}$. Its symmetry group is $O(n)$, $n\times n$ orthogonal |