Self-avoiding walk, spin systems and renormalization

The self-avoiding walk, and lattice spin systems such as the φ(4) model, are models of interest both in mathematics and in physics. Many of their important mathematical problems remain unsolved, particularly those involving critical exponents. We survey some of these problems, and report on recent a...

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Detalles Bibliográficos
Autor principal: Slade, Gordon
Formato: Online Artículo Texto
Lenguaje:English
Publicado: The Royal Society Publishing 2019
Materias:
Perspective
Acceso en línea:https://www.ncbi.nlm.nih.gov/pmc/articles/PMC6364616/
https://www.ncbi.nlm.nih.gov/pubmed/30760959
http://dx.doi.org/10.1098/rspa.2018.0549
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author Slade, Gordon
author_facet Slade, Gordon
author_sort Slade, Gordon
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description The self-avoiding walk, and lattice spin systems such as the φ(4) model, are models of interest both in mathematics and in physics. Many of their important mathematical problems remain unsolved, particularly those involving critical exponents. We survey some of these problems, and report on recent advances in their mathematical understanding via a rigorous non-perturbative renormalization group method.
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spelling pubmed-63646162019-02-13 Self-avoiding walk, spin systems and renormalization Slade, Gordon Proc Math Phys Eng Sci Perspective The self-avoiding walk, and lattice spin systems such as the φ(4) model, are models of interest both in mathematics and in physics. Many of their important mathematical problems remain unsolved, particularly those involving critical exponents. We survey some of these problems, and report on recent advances in their mathematical understanding via a rigorous non-perturbative renormalization group method. The Royal Society Publishing 2019-01 2019-01-23 /pmc/articles/PMC6364616/ /pubmed/30760959 http://dx.doi.org/10.1098/rspa.2018.0549 Text en © 2019 The Authors. http://creativecommons.org/licenses/by/4.0/ Published by the Royal Society under the terms of the Creative Commons Attribution License http://creativecommons.org/licenses/by/4.0/, which permits unrestricted use, provided the original author and source are credited.
spellingShingle Perspective
Slade, Gordon
Self-avoiding walk, spin systems and renormalization
title Self-avoiding walk, spin systems and renormalization
title_full Self-avoiding walk, spin systems and renormalization
title_fullStr Self-avoiding walk, spin systems and renormalization
title_full_unstemmed Self-avoiding walk, spin systems and renormalization
title_short Self-avoiding walk, spin systems and renormalization
title_sort self-avoiding walk, spin systems and renormalization
topic Perspective
url https://www.ncbi.nlm.nih.gov/pmc/articles/PMC6364616/
https://www.ncbi.nlm.nih.gov/pubmed/30760959
http://dx.doi.org/10.1098/rspa.2018.0549
work_keys_str_mv AT sladegordon selfavoidingwalkspinsystemsandrenormalization

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