Physics – Condensed Matter – Statistical Mechanics
Scientific paper
2010-05-08
Nucl.Phys.B843:255-301,2011; Erratum-ibid.B853:210-211,2011
Physics
Condensed Matter
Statistical Mechanics
Latex source file with 8 eps files, 45 pages, 7 figures; v2: minor changes, misprints corrected
Scientific paper
10.1016/j.nuclphysb.2010.09.005
The theory of generalized local scale invariance of strongly anisotropic scale invariant systems proposed some time ago by Henkel [Nucl. Phys. B \textbf{641}, 405 (2002)] is examined. The case of so-called type-I systems is considered. This was conjectured to be realized by systems at m-axial Lifshitz points; in support of this claim, scaling functions of two-point cumulants at the uniaxial Lifshitz point of the three-dimensional ANNNI model were predicted on the basis of this theory and found to be in excellent agreement with Monte Carlo results [Phys. Rev. Lett. \textbf{87}, 125702 (2001)]. The consequences of the conjectured invariance equations are investigated. It is shown that fewer solutions than anticipated by Henkel generally exist and contribute to the scaling functions if these equations are assumed to hold for all (positive and negative) values of the d-dimensional space (or space time) coordinates $(t,\bm{r})\in \mathbb{R}\times\mathbb{R}^{d-1}$. Specifically, a single rather than two independent solutions exists in the case relevant for the mentioned fit of Monte Carlo data for the ANNNI model. Renormalization-group improved perturbation theory in $4+m/2-\epsilon$ dimensions is used to determine the scaling functions of the order-parameter and energy-density two-point cumulants in momentum space to two-loop order. The results are mathematically incompatible with Henkel's predictions except in free-field-theory cases. However, the scaling function of the energy-density cumulant we obtain for m=1 upon extrapolation of our two-loop RG results to d=3 differs numerically little from that of an effective free field theory.
Diehl H. W.
Rutkevich Sergei
Shpot M. A.
No associations
LandOfFree
On conjectured local generalizations of anisotropic scale invariance and their implications 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 On conjectured local generalizations of anisotropic scale invariance and their implications, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and On conjectured local generalizations of anisotropic scale invariance and their implications will most certainly appreciate the feedback.
Profile ID: LFWR-SCP-O-303446