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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2D Ising model according to Eq ansatz average calculations Chapter conﬁgurations contribution correlation function correlation length corresponding critical behavior critical exponents critical phenomena critical point deﬁned deﬁnition described diagram dimensions directed polymer distribution function P(q easily check energy barriers exponentially external magnetic ﬁeld ferromagnetic ﬁeld h ﬁnally ﬁnds ﬁnite ﬁrst ﬁxed point ﬂuctuations free energy Gaussian Hamiltonian impurities inﬁnite instanton integration Ising model lattice Let us consider local minima macroscopic mean-ﬁeld theory minima non-trivial non-zero obtained one-step RSB order parameter overlaps paramagnetic Parisi partition function phase transition phase transition point physical problem properties pure system qualitative quantity quenched disorder random ﬁeld Ising random potential region renormalization replica free energy replica partition function replica symmetry breaking result RG equations saddle-point equation scale Section singularities spatial speciﬁc heat spin systems statistical mechanics strong coupling regime structure summation thermal ultrametric vector wandering exponent zero