Critical phenomena and renormalization-group theory
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Publication:1615004
DOI10.1016/S0370-1573(02)00219-3zbMATH Open0997.82019arXivcond-mat/0012164OpenAlexW3104925330WikidataQ57319750 ScholiaQ57319750MaRDI QIDQ1615004
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Publication date: 10 September 2002
Published in: (Search for Journal in Brave)
Abstract: We review results concerning the critical behavior of spin systems at equilibrium. We consider the Ising and the general O()-symmetric universality classes, including the limit that describes the critical behavior of self-avoiding walks. For each of them, we review the estimates of the critical exponents, of the equation of state, of several amplitude ratios, and of the two-point function of the order parameter. We report results in three and two dimensions. We discuss the crossover phenomena that are observed in this class of systems. In particular, we review the field-theoretical and numerical studies of systems with medium-range interactions. Moreover, we consider several examples of magnetic and structural phase transitions, which are described by more complex Landau-Ginzburg-Wilson Hamiltonians, such as -component systems with cubic anisotropy, O()-symmetric systems in the presence of quenched disorder, frustrated spin systems with noncollinear or canted order, and finally, a class of systems described by the tetragonal Landau-Ginzburg-Wilson Hamiltonian with three quartic couplings. The results for the tetragonal Hamiltonian are original, in particular we present the six-loop perturbative series for the -functions. Finally, we consider a Hamiltonian with symmetry that is relevant for the description of multicritical phenomena.
Full work available at URL: https://arxiv.org/abs/cond-mat/0012164
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