Incollection,
Critical phenomena described by Landau-Ginzburg-Wilson $\Phi^4$ theories with several couplings
Abstract Book of the XXIII IUPAP International Conference on Statistical Physics, Genova, Italy, (9-13 July 2007)
Abstract
In the framework of the renormalization-group (RG) theory of critical
phenomena, a quantitative description of many continuous phase transitions can
be obtained by considering an effective Landau-Ginzburg-Wilson (LGW) $\Phi^4$
theories, having an $N$-component fundamental field $\Phi_i$ and containing up
to fourth-order powers of the field components,
eqnarray
H =
12 \sum_i (\partial_\Phi_i)^2 +
12 \sum_i r_i \Phi_i^2 +
14! \sum_ijkl u_ijkl \; \Phi_i\Phi_j\Phi_k\Phi_l
eqnarray
The study of the critical behavior of several physically interesting systems
requires LGW $\Phi^4$ theories with several quadratic and quartic parameters,
depending on the symmetry and symmetry-breaking pattern. I mention
transitions in disordered spin systems, magnets with impurities, frustrated
systems with noncollinear order, stacked triangular antiferromagnets,
$^3$He, hadronic matter, etc..., and also multicritical behaviors due to
the competition of different order parameters, when different critical lines
meet, as in anisotropic antiferromagnets, high-$T_c$ superconductors, etc...
I present an overview of our recent field-theory results (obtained by
computing and analyzing high-order perturbative series)
for physically interesting generalized LGW theories, related to
various transitions in different contexts, and compare them with the best
experimental estimates and theoretical results obtained by other approaches,
such as Monte Carlo simulations. I also discuss the conjecture that the
stable fixed point in the RG flow of general LGW theories corresponds to the
fastest decay of correlations, that is, is the one with the largest values of
the critical exponent $\eta$.
Some of our recent relevant works, whose results will be mentioned,
are: EV, J. Zinn-Justin, Fixed point stability and decay of
correlations, New Journal of Phys. 8 (2006) 321 cond-mat/0611353. M. De
Prato, A. Pelissetto, EV, Spin-density-wave order in cuprates, Phys.
Rev. B 74 (2006) 144507 cond-mat/0601404. M. Hasenbusch, A. Pelissetto, EV,
Instability of the O(5) critical behavior in the SO(5) theory of
high-$T_c$ superconductors, Phys. Rev. B 72 (2005) 014532
cond-mat/0502327. P. Calabrese, A. Pelissetto, EV, Multicritical
behavior in frustrated spin systems with noncollinear order, Nucl. Phys. B
709 (2005) 550 cond-mat/0408130. M. Hasenbusch, F. Parisen Toldin, A.
Pelissetto, EV, Universality class of 3D site-diluted and bond-diluted
Ising systems, J. Stat. Mech.: Theory Exp. (2007) P02016
cond-mat/0611707; The 3D $J$ Ising model at the ferromagnetic
transition line, in preparation. A. Pelissetto, EV, Multicritical
behavior of two-dimensional antiferromagnets in a magnetic field
cond-mat/0702273.
Tags
- behavior
- critical
- disordered
- group
- landau-ginzburg-wilson
- models
- multicritical
- phenomena
- renormalization
- statphys23
- theories
- topic-2
