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

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13번째 줄: 13번째 줄:
 
** a : lattice spacing
 
** a : lattice spacing
 
** V : volume
 
** V : volume
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* scaling limit
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* scaling limit<br>
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** sending the lattice spacing a to zero, , while keeping the volume V=Na constant
 
*  continuum limit<br>
 
*  continuum limit<br>
 
**  sending the lattice spacing a to zero, and the number N of sites to infinity, while keeping the volume V=Na constant<br>
 
**  sending the lattice spacing a to zero, and the number N of sites to infinity, while keeping the volume V=Na constant<br>
 
*  thermodynamic limit<br>
 
*  thermodynamic limit<br>
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**  the size of the quantizing system to infinity<br>
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**  a model is taken to the thermodynamic limit by increasing the volume together with the particle number so that the average particle number density remains constant.<br>
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** [http://en.wikipedia.org/wiki/Thermodynamic_limit ]http://en.wikipedia.org/wiki/Thermodynamic_limit<br>
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** http://en.wikipedia.org/wiki/Thermodynamic_limit<br>
 
*  infrared limit<br>
 
*  infrared limit<br>
 
**  sending V to infinity, while keeping a constant<br>
 
**  sending V to infinity, while keeping a constant<br>
35번째 줄: 36번째 줄:
 
 
 
 
  
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<h5>m</h5>
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<h5>memo</h5>
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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)<br> # Newman, C.M.: Normal fluctuations and the FKG inequalities. Commun. Math. Phys.74, 119 (1980)<br> # Fröhlich, J., Spencer, T.: Some recent rigorous results in the theory of phase transitions and critical phenomena. Séminaire Bourbaki No. 586 (February 1982)<br> # 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
  
 
 
 
 

2010년 8월 19일 (목) 21:32 판

introduction

 

 

 

concept of limit
  • notations
    • N : number of sites
    • a : lattice spacing
    • V : volume
  • scaling limit
    • sending the lattice spacing a to zero, , while keeping the volume V=Na constant
  • continuum limit
    • sending the lattice spacing a to zero, and the number N of sites to infinity, while keeping the volume V=Na constant
  • thermodynamic limit
  • infrared limit
    • sending V to infinity, while keeping 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
  1. 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

 

 

 

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