Physics – Condensed Matter – Statistical Mechanics
Scientific paper
2005-12-28
J. Phys. A: Math. Gen. 39 (2006) 7927-7942
Physics
Condensed Matter
Statistical Mechanics
submitted to J. Phys. A: Math and Gen, special issue on Renormalization Group 2005 as featured in the international workshop
Scientific paper
10.1088/0305-4470/39/25/S09
Semi-infinite $d$-dimensional systems with an $m$-axial bulk Lifshitz point are considered whose ($d-1$)-dimensional surface hyper-plane is oriented perpendicular to one of the $m$ modulation axes. An $n$-component $\phi^4$ field theory describing the bulk and boundary critical behaviour when (i) the Hamiltonian can be taken to have O(n) symmetry and (ii) spatial anisotropies breaking its Euclidean symmetry in the $m$-dimensional coordinate subspace of potential modulation directions may be ignored is investigated. The long-distance behaviour at the ordinary surface transition is mapped onto a field theory with the boundary conditions that both the order parameter $\bm{\phi}$ and its normal derivative $\partial_n\bm{\phi}$ vanish at the surface plane. The boundary-operator expansion is utilized to study the short-distance behaviour of $\bm{\phi}$ near the surface. Its leading contribution is found to be controlled by the boundary operator $\partial_n^2\bm{\phi}$. The field theory is renormalized for dimensions $d$ below the upper critical dimension $d^*(m)=4+m/2$, with a corresponding surface source term $\propto \partial_n^2\bm{\phi}$ added. The anomalous dimension of this boundary operator is computed to first order in $\epsilon=d^*-d$. The result is used in conjunction with scaling laws to estimate the value of the single independent surface critical exponent $\beta_{\mathrm{L}1}^{(\mathrm{ord},\perp)}$ for $d=3$. Our estimate for the case $m=n=1$ of a uniaxial Lifshitz point in Ising systems is in reasonable agreement with published Monte Carlo results.
Diehl H. W.
Prudnikov Pavel V.
Shpot M. A.
No associations
LandOfFree
Boundary critical behaviour at m-axial Lifshitz points of semi-infinite systems with a surface plane perpendicular to a modulation axis 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 Boundary critical behaviour at m-axial Lifshitz points of semi-infinite systems with a surface plane perpendicular to a modulation axis, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Boundary critical behaviour at m-axial Lifshitz points of semi-infinite systems with a surface plane perpendicular to a modulation axis will most certainly appreciate the feedback.
Profile ID: LFWR-SCP-O-668928