Communications in Mathematical Physics - Volume 238 by M. Aizenman (Chief Editor)

By M. Aizenman (Chief Editor)

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Furthermore, we give estimates on the difference between the values of parameters of the actual model and its mean-field counterpart at their corresponding transitions and show that these differences tend to zero as the spatial dimension tends to infinity. In short, mean field theory is quantitatively accurate whenever the dimension is sufficiently large. Phase Transitions and Mean-Field Theory 55 The main driving force of our proofs is the availability of the so called infrared bound [18,22–24], which we use for estimating the correlations between nearest-neighbor spins.

5. Mean-Field Theory and Complete-Graph Models . . M. Biskup, L. Chayes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 68 71 74 76 76 76 77 78 79 82 84 90 1. 1. Motivation and outline. Mean-field theory has traditionally played a seminal role for qualitative understanding of phase transitions. In fact, most practical studies of complex physical systems begin (and sometimes end) with the analysis of the corresponding mean field theory.

Mirror symmetry for open strings. Phys. Rev. D (3) 62, (2000) 16. : Enhanced gauge symmetry in type II string theory. Nucl. Phys. B 477, 105–140 (1996) 17. : A note on words in braid monoids. J. Algebra 215, 366–377 (1999) 18. : Compactifications of F -theory on Calabi–Yau threefolds I, II. Nuc. Phys. B 473, 74–92 (1996); Nucl. Phys. B 476, 437–469 (1996) 19. : Braid group actions on derived categories of coherent sheaves. Duke Math. J. 108, 37–108 (2001) 20. : Calabi–Yau threefolds with a curve of singularities and counterexamples to the Torelli problem II.

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