# Édouard Brézin

## From Wikipedia, the free encyclopedia

Édouard Brezin | |
---|---|

Born | |

Nationality | French |

Alma mater | École Polytechnique École des ponts ParisTech |

Scientific career | |

Fields | Physics |

**Édouard Brézin** (French: [bʁezɛ̃]; born 1 December 1938 Paris) is a French theoretical physicist. He is professor at Université Paris 6, working at the laboratory for theoretical physics (LPT) of the École Normale Supérieure since 1986.

## Biography

Brézin was born in Paris, France, to a family of Jewish background.^{[1]} He studied at École Polytechnique before doing a PhD. He worked at the theory division of the *Commissariat à l'énergie atomique* in Saclay until 1986.^{[citation needed]}

Brezin contributed to the field of physics that deals with the macroscopic physical properties of matter and high energy physics. He was a leader in critical behavior theory and developed methods for distilling testable predictions for critical exponents. In using field theoretic techniques in the study of condensed matter, Brezin helped further modern theories of magnetism and the quantum Hall effect.

Brézin was elected a member of the French Academy of Sciences on 18 February 1991 and served as president of the academy in 2005-2006. He also is a foreign associate of the United States National Academy of Sciences (since 2003), a foreign honorary member of the American Academy of Arts and Sciences (since 2002), a foreign member of the Royal Society (since 2006) and a member of the Academia Europaea (since 2003). He is a commander in the French National order of merit^{[2]} and an Officer of the Legion of Honor.^{[3]}

He is Chair of the Cyprus Research and Educational Foundation.^{[4]}
He was awarded the 2011 Dirac Medal of the International Centre for Theoretical Physics together with John Cardy and Alexander Zamolodchikov.

In 2004 he won the Institute of Physics President's Medal.^{[5]}

## Research work

Edouard Brezin's work is devoted to quantum field theory, mainly for applications in statistical physics (E. Brezin et S. Wadia, The large N expansion in quantum field theory and statistical physics : from spin systems to two-dimensional quantum gravity, World Scientific, 1993). It uses the theoretical formulation of the renormalization group for critical phenomena (equation of states, scaling corrections, etc.). He showed that the low temperature phase, in the case of a continuous symmetry break, is described by a non-linear sigma model, leading to a development of critical exponents in powers of the minus two space dimension. He showed that the instantaneous method can be used to characterize the asymptotic behaviour of perturbation theory, thus allowing accurate theoretical estimates to be made (E.Brezin, Fields, strings and critical phenomena, North Holland, Les Houches, 1988). He has applied field theory techniques to condensed matter problems, such as critical wetting theory or the study of the phase transition from a normal metal to a type II superconductor under magnetic field. He became interested in theories of gauging with a large number of colors. This led to a representation of two-dimensional quantum gravity by random fluctuating surfaces or closed bosonic strings, in terms of random matrices (E Brezin et S. Hikami, Random matrix theory with an external source, Springer, 2016). He showed that the continuous boundary of such models is linked to integrable hierarchies such as KdV flows. He has also worked on establishing the universality of eigenvalue correlations for random matrices (« Edoaud Brezin, membre de l'Académie des sciences » [archive], sur Académie des sciences (consulté le 9 novembre 2018)).

## Notable publications

- E Brezin and C Itzykson, "
*Pair production in vacuum by an alternating field*". Physical Review D 2 (1970) 1191 - E Brezin, DJ Wallace and KG Wilson, "
*Feynman-graph expansion for the equation of state near the critical point*" Physical Review Letters 29 (1972) 591 - E Brezin, JC Le Guillou and J Zinn-Justin "
*Wilson's theory of critical phenomena and Callan-Symanzik equations in 4-epsilon dimension*". Physical Review D 8 (1973) 434. - E Brezin and J Zinn-Justin, "
*Renormalization of the non-linear sigma model in 2+epsilon dimension ; application to the Heisenberg ferromagnets*". Physical Review Letters 36 (1976) 691 - E Brezin, C Itzykson, G Parisi and JB Zuber "
*Planar diagrams*". Comm. in Math. Phys. 59 (1978) 35 - E Brezin, DJ Gross "
*The external field problem in the large N limit of QCD*". Physics Letters B 97 (1980)120 - E Brezin, B Halperin and S Leibler, "
*Critical wetting in 3 dimensions*". Physical Review Letters 50 (1983) 1387 - E Brezin, DJ Gross and C Itzykson, "
*Density of states in the presence of a strong magnetic field and random impurities*". Nucl. Phys. B 235[FS11] (1984) 24 - E Brezin, DR Nelson and A Thiaville "
*Fluctuation effects near Hc2 in type II superconductors*". Phys. Rev. B 31 (1985) 7124 - E Brezin and V Kazakov, "
*Exactly solvable field theories of closed strings*".Phys. Letters B236(1990)144 - E Brezin and A Zee, "
*Universality of the correlations between eigenvalues of random matrices*". Nucl. Phys. B 402 (1993) 613 - E Brezin and S Hikami, "
*Intersection numbers of Riemann surfaces from Gaussian matrix models*". Comm. Math. Phys. 283 (2008) 507

## Books

*The large N expansion in quantum field theory and statistical physics*, E Brezin and S Wadia, World Scientific (1993)*Introduction to statistical field theory*, E Brezin, Cambridge University press (2010)

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