Introduction to the Replica Theory of Disordered Statistical Systems
Cambridge University Press, 13 окт. 2005 г. - Всего страниц: 236
This text describes the statistical mechanics of classical spin systems with quenched disorder. The first part covers the physics of spin-glass states using results obtained within the framework of the mean field theory of spin glasses. The second part is devoted to the theory of critical phenomena in the presence of weak quenched disorder. This includes a systematic derivation of the traditional renormalization group theory. In the third part Dotsenko describes other types of disordered systems, relating them to new results at the frontiers of modern research. The book is suitable for graduate students and researchers in the field of statistical mechanics of disordered systems.
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appears approach assumed average barriers becomes calculations Chapter close condition conﬁgurations considered continuous contribution correlation correlation function corresponding critical critical behavior critical exponents critical point deﬁned demonstrate depend described dimensions directed disorder distribution function easily effects equal equation exist ferromagnetic ﬁeld ﬁnds ﬁnite ﬁrst ﬁxed point ﬂuctuations free energy given gives glasses ground Hamiltonian hand inﬁnite integration interactions interval Ising model length limit magnetic ﬁeld matrix mean-ﬁeld means method minima Note obtained order parameter original parameter particular partition function phase transition phenomena physical possible present probability problem properties pure system qualitative quantity quenched random region replica result saddle-point equation scale separated shown simple singularities situation solution space speciﬁc heat spin spin-glass statistical structure taken temperature theory thermodynamic usual zero