Ettore Vicari

Critical phenomena and renormalization-group theory

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.

Critical behavior of the three-dimensional XY universality class

We improve the theoretical estimates of the critical exponents for the three-dimensional XY universality class. We find alpha=-0.0146(8), gamma=1.3177(5), nu=0.67155(27), eta=0.0380(4), beta=0.3485(2), and delta=4.780(2). We observe a discrepancy with the most recent experimental estimate of alpha; this discrepancy calls for further theoretical and experimental investigations. Our results are obtained by combining Monte Carlo simulations based on finite-size scaling methods, and high-temperature expansions. Two improved models (with suppressed leading scaling corrections) are selected by Monte Carlo computation. The critical exponents are computed from high-temperature expansions specialized to these improved models. By the same technique we determine the coefficients of the small-magnetization expansion of the equation of state. This expansion is extended analytically by means of approximate parametric representations, obtaining the equation of state in the whole critical region. We also determine the specific-heat amplitude ratio.

Critical exponents and equation of state of the three-dimensional Heisenberg universality class

We improve the theoretical estimates of the critical exponents for the three-dimensional Heisenberg universality class. We find gamma=1.3960(9), nu=0.7112(5), eta=0.0375(5), alpha=-0.1336(15), beta=0.3689(3), and delta=4.783(3). We consider an improved lattice phi^4 Hamiltonian with suppressed leading scaling corrections. Our results are obtained by combining Monte Carlo simulations based on finite-size scaling methods and high-temperature expansions. The critical exponents are computed from high-temperature expansions specialized to the phi^4 improved model. By the same technique we determine the coefficients of the small-magnetization expansion of the equation of state. This expansion is extended analytically by means of approximate parametric representations, obtaining the equation of state in the whole critical region. We also determine a number of universal amplitude ratios.

Theta dependence of SU(N) gauge theories

We study the

Theta dependence of SU(N) gauge theories in the presence of a topological term

\theta

25th-order high-temperature expansion results for three-dimensional Ising-like systems on the simple cubic lattice

dependence of four-dimensional SU(

Theoretical estimates of the critical exponents of the superfluid transition in {sup 4}He by lattice methods

N

Spectrum of confining strings in SU(N) gauge theories

) gauge theories, for

Topological charge, renormalization and cooling on the lattice☆

N\geq 3

Randomly dilute spin models: A six-loop field-theoretic study

and in the large-N limit. We use numerical simulations of the Wilson lattice formulation of gauge theories to compute the first few terms of the expansion of the ground-state energy