"Various concepts of limit in statistical physics"의 두 판 사이의 차이

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(피타고라스님이 이 페이지의 이름을 concept of limit in statistical physics로 바꾸었습니다.)
 
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==introduction==
  
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==concept of limit==
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===notations===
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* N : number of sites
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* a : lattice spacing
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* V : volume
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===continuum limit===
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*  used in the lattice model
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*  sending the lattice spacing a to zero, and the number N of sites to infinity, while keeping the volume V=Na constant
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* applied to spin chains whose continuum limit yields conformal field theories
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=== scaling limit===
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* sounds similar to continuum limit
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* sending the lattice spacing a to zero, while keeping the volume V and the correlation length fixed
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===thermodynamic limit===
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*  increasing the volume together with the particle number so that the average particle number density remains constant.
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* http://en.wikipedia.org/wiki/Thermodynamic_limit
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===infrared limit===
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*  sending V to infinity, while keeping the lattice spacing a constant
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===ultraviolet limit===
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*  ??
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The c-theorem implies that the infra-red limit, where the scale goes to innity, and the ultra-violet limit, where the scale vanishes, are fixed points of the renormalisation group.
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http://iopscience.iop.org/1126-6708/2000/03/008/pdf/1126-6708_2000_03_008.pdf
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==memo==
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* Glimm, J., Jaffe, A.: [http://www.springerlink.com/content/t413601r24427883/ Particles and scaling for lattice fields and Ising models]. Commun. Math. Phys.51, 1 (1976)
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* Newman, C.M.: Normal fluctuations and the FKG inequalities. Commun. Math. Phys.74, 119 (1980)
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* Fröhlich, J., Spencer, T.: Some recent rigorous results in the theory of phase transitions and critical phenomena. Séminaire Bourbaki No. 586 (February 1982)
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* Sinai, Ya.G.: Mathematical foundations of the renormalization group method in statistical physics. In: Mathematical problems in theoretical physics. Dell'Antonio, G., Doplicher, S., Jona-Lasinio, G. (eds.). Lectures Notes in Physics, Vol. 80. Berlin, Heidelberg, New York: Springer 1978
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[[분류:개인노트]]
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[[분류:physics]]
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[[분류:math and physics]]
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[[분류:migrate]]
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==메타데이터==
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===위키데이터===
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* ID :  [https://www.wikidata.org/wiki/Q1103484 Q1103484]
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===Spacy 패턴 목록===
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* [{'LOWER': 'thermodynamic'}, {'LEMMA': 'limit'}]

2021년 2월 17일 (수) 02:31 기준 최신판

introduction

concept of limit

notations

  • N : number of sites
  • a : lattice spacing
  • V : volume

continuum limit

  • used in the lattice model
  • sending the lattice spacing a to zero, and the number N of sites to infinity, while keeping the volume V=Na constant
  • applied to spin chains whose continuum limit yields conformal field theories

scaling limit

  • sounds similar to continuum limit
  • sending the lattice spacing a to zero, while keeping the volume V and the correlation length fixed

thermodynamic limit

infrared limit

  • sending V to infinity, while keeping the lattice spacing a constant

ultraviolet limit

  • ??



The c-theorem implies that the infra-red limit, where the scale goes to innity, and the ultra-violet limit, where the scale vanishes, are fixed points of the renormalisation group.

http://iopscience.iop.org/1126-6708/2000/03/008/pdf/1126-6708_2000_03_008.pdf



memo

  • Glimm, J., Jaffe, A.: Particles and scaling for lattice fields and Ising models. Commun. Math. Phys.51, 1 (1976)
  • Newman, C.M.: Normal fluctuations and the FKG inequalities. Commun. Math. Phys.74, 119 (1980)
  • Fröhlich, J., Spencer, T.: Some recent rigorous results in the theory of phase transitions and critical phenomena. Séminaire Bourbaki No. 586 (February 1982)
  • Sinai, Ya.G.: Mathematical foundations of the renormalization group method in statistical physics. In: Mathematical problems in theoretical physics. Dell'Antonio, G., Doplicher, S., Jona-Lasinio, G. (eds.). Lectures Notes in Physics, Vol. 80. Berlin, Heidelberg, New York: Springer 1978

메타데이터

위키데이터

Spacy 패턴 목록

  • [{'LOWER': 'thermodynamic'}, {'LEMMA': 'limit'}]
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