Critical Phenomena and Renormalization-Group Theory

Physics – Condensed Matter – Statistical Mechanics

Scientific paper

Rate now

  [ 0.00 ] – not rated yet Voters 0   Comments 0

Details

151 pages. Extended and updated version. To be published in Physics Reports

Scientific paper

10.1016/S0370-1573(02)00219-3

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 $N\to 0$ 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 $\beta$-functions. Finally, we consider a Hamiltonian with symmetry $O(n_1)\oplus O(n_2)$ that is relevant for the description of multicritical phenomena.

No associations

LandOfFree

Say what you really think

Search LandOfFree.com for scientists and scientific papers. Rate them and share your experience with other people.

Rating

Critical Phenomena and Renormalization-Group Theory does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with Critical Phenomena and Renormalization-Group Theory, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Critical Phenomena and Renormalization-Group Theory will most certainly appreciate the feedback.

Rate now

     

Profile ID: LFWR-SCP-O-686915

  Search
All data on this website is collected from public sources. Our data reflects the most accurate information available at the time of publication.