Victor Dotsenko

Université Pierre et Marie Curie
Long standing problem of the nature of the phase transitions in weakly disordered Ising-like statistical systems [1] is considered from the point of view of the recent developments in the replica method [2]. In particular, non-perturbative [3] and non-selfaveraging [4] phenomena in the critical point are considered, as well as the possibility of the universal probability distribution function for non-self averaging free energy critical fluctuations is discussed [5].
[1] V. Dotsenko. Critical phenomena and quenched disorder. Physics-Uspekhi, 38, No.5 (1995) 457; V. Dotsenko. Introduction to the Replica Theory of Disordered Statistical Systems. Cambridge University Press, 2001.
[2] V. Dotsenko. One more discussion of the replica trick: the example of the exact solution. Philosophical Magazine, 92, (2012) 16; V. Dotsenko. Replica solution of the Random Energy Model. EPL, 95, (2011) 50006; V. Dotsenko. Universal Randomness. Physics-Uspekhi, 54, (2011) 259.
[3] V. Dotsenko. Non-pertrurbative states in disordered systems. Phys. A, 361, (2006) 463.
[4] S. Wiseman, E. Domany. Lack of self-averaging in critical disordered systems. Phys. Rev. E, 52 (1995) 3469; A. Aharony, B. Harris. Absence of self-averaging and universal fluctuations in random systems near critical points. Phys. Rev. Lett. 77, (1996) 3700; S. Wiseman, E. Domany. Finite-size scaling and lack of self-averaging in critical disordered systems. Phys. Rev. Lett. 81, (1998) 22.
[5] V. Dotsenko, B. Klumov. Free Energy Distribution Function of a Random Ising ferromagnet. J. Stat. Mech. (2012) P05027.
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