Critical phenomena and renormalization-group theory

By A. Pelissetto, E. Vicari. 2000

1,392 citations recorded by the source corpus.

Abstract We review results concerning the critical behavior of spin systems at equilibrium. We consider the Ising and the general O ( N )-symmetric universality classes, including the N →0 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 N -component systems with cubic anisotropy, O ( N )-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 β -functions. Finally, we consider a Hamiltonian with symmetry O ( n 1 )⊕ O ( n 2 ) that is relevant for the description of multicritical phenomena.

Subfields: Atomic and Molecular Physics, and Optics, Condensed Matter Physics

View Paper: https://www.semanticscholar.org/paper/03e916db0a8b87028a765c0edc0dff52d6b9ace7

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Citations in the corpus

Critical exponents of the 3d Ising and related models from conformal bootstrap (2014, background): “These scaling dimensions are related to the conventional critical exponents by η = 2∆σ − 1, ν = 1/(3−∆ε), ω = ∆ε′ − 3 and ωNR = ∆4 − 3, where η is the magnetic exponent, ν the thermal exponent, ω is the exponent controlling the scaling corrections of rotationally invariant operators and finally ωNR ”
An Asymptotically Safe Guide to Quantum Gravity and Matter (2018, methodology): “It has been characterized with various methods (Guida and Zinn-Justin, 1998; Campostrini et al., 1999; Pelissetto and Vicari, 2002; Canet et al., 2003; Litim and Zappala, 2011; ElShowk et al., 2012, 2014; Gliozzi and Rago, 2014) and serves as a benchmark example for many techniques.”
Bootstrapping the O(N ) vector models (2013, background): “J H E P 0 6 ( 2 0 1 4 ) 0 9 1 are the critical O(N) vector models [17, 18], which describe second-order phase transitions in a variety of real-world systems at small values of N [19], and are also solvable in a 1/N expansion at large values of N (see [20] for a review).”
The nonperturbative functional renormalization group and its applications (2020, background): “systems in the vicinity of a second-order phase transition [9, 14, 15].”
Mapping the phases of quantum chromodynamics with beam energy scan (2019, neutral): “[82–84]).”
Critical phenomena in microgravity: Past, present, and future (2007, background): “…RG theory can be obtained from textbooks and extensive reviews on the subject and references therein Fisher, 1974, 1998; Ma, 1976; Parisi, 1988; Itzykson and DrouHe, 1989; Binney et al., 1993; Cardy, 1996; Kleinert and Schulte-Frohlinde, 2001; Zinn-Justin, 2001, 2002; Pelissetto and Vicari, 2002 .”
Walking, weak first-order transitions, and complex CFTs (2018, background): “enomenon is the collision between the cubic and the O(N) xed points of multield scalar theories in 4 dimensions, which pass through each other interchanging stability at some Nc= 4 + O() ([59] and [60], section 11.3). Notice that the collision with free theories discussed above can also be viewed as”
theta dependence of SU(N) gauge theories in the presence of a topological term (2007, background): “tially because the expected symmetry breaking SU(2)L ⊗ SU(2)R → SU(2)V is equivalent to O(4) → O(3), as in the O(4) vector model), characterizedby the critical exponents ν= 0.749(2) and η= 0.0365(10) [296,445]. The transition can be continuous also in the case the U(1)A symmetry is eﬀectively restor”
Bootstrapping mixed correlators in the 3D Ising model (2014, neutral): “5 by resumming the ǫ-expansion [84], ∆σ′ ≈ 5.”