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zbMATH Open
Article . 2016
Data sources: zbMATH Open
Bulletin of the London Mathematical Society
Article . 2016 . Peer-reviewed
Data sources: Crossref
https://dx.doi.org/10.48550/ar...
Article . 2015
License: arXiv Non-Exclusive Distribution
Data sources: Datacite
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A dimer ABC:

A dimer ABC
Authors: Bocklandt, Raf;
Abstract

We give an overview of recent developments in the theory of dimer models. The viewpoint we take is inspired by mirror symmetry. After an introduction to the combinatorics of dimer models, we will first look at dimers in dynamical systems and statistical mechanics, which can be viewed as coming from the A-model in mirror symmetry. Then we will discuss the role of dimers in the theory of resolutions of singularities, which is inspired by the B-model. The C stands for the connections that tie both subjects together: clusters, categories, and stability conditions. In this final part we will give some ideas on how these two stories fit in a broader framework.

Related Organizations
Keywords

graph theory, perfect matching, square lattice, FOS: Physical sciences, Mathematical Physics (math-ph), Phase transitions (general) in equilibrium statistical mechanics, Lattice systems (Ising, dimer, Potts, etc.) and systems on graphs arising in equilibrium statistical mechanics, Graph theory (educational aspects), phase transitions, Mathematics - Algebraic Geometry, FOS: Mathematics, clusters, Representation Theory (math.RT), Algebraic Geometry (math.AG), Mathematics - Representation Theory, Mathematical Physics

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    selected citations
    These citations are derived from selected sources.
    This is an alternative to the "Influence" indicator, which also reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
    15
    popularity
    This indicator reflects the "current" impact/attention (the "hype") of an article in the research community at large, based on the underlying citation network.
    Top 10%
    influence
    This indicator reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
    Top 10%
    impulse
    This indicator reflects the initial momentum of an article directly after its publication, based on the underlying citation network.
    Top 10%
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selected citations
These citations are derived from selected sources.
This is an alternative to the "Influence" indicator, which also reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
BIP!Citations provided by BIP!
popularity
This indicator reflects the "current" impact/attention (the "hype") of an article in the research community at large, based on the underlying citation network.
BIP!Popularity provided by BIP!
influence
This indicator reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
BIP!Influence provided by BIP!
impulse
This indicator reflects the initial momentum of an article directly after its publication, based on the underlying citation network.
BIP!Impulse provided by BIP!
15
Top 10%
Top 10%
Top 10%
Green
bronze