Critical behavior at m-axial Lifshitz points: field-theory analysis and $ε$-expansion results

dc.creatorDiehl, H. W.
dc.creatorShpot, M.
dc.date2000-06-01
dc.date2000-06-13
dc.date.accessioned2026-07-07T12:16:32Z
dc.date.available2026-07-07T12:16:32Z
dc.descriptionThe critical behavior of d-dimensional systems with an n-component order parameter is reconsidered at (m,d,n)-Lifshitz points, where a wave-vector instability occurs in an m-dimensional subspace of ${\mathbb R}^d$. Our aim is to sort out which ones of the previously published partly contradictory $ε$-expansion results to second order in $ε=4+\frac{m}{2}-d$ are correct. To this end, a field-theory calculation is performed directly in the position space of $d=4+\frac{m}{2}-ε$ dimensions, using dimensional regularization and minimal subtraction of ultraviolet poles. The residua of the dimensionally regularized integrals that are required to determine the series expansions of the correlation exponents $η_{l2}$ and $η_{l4}$ and of the wave-vector exponent $β_q$ to order $ε^2$ are reduced to single integrals, which for general m=1,...,d-1 can be computed numerically, and for special values of m, analytically. Our results are at variance with the original predictions for general m. For m=2 and m=6, we confirm the results of Sak and Grest [Phys. Rev. B {\bf 17}, 3602 (1978)] and Mergulh{ã}o and Carneiro's recent field-theory analysis [Phys. Rev. B {\bf 59},13954 (1999)].
dc.descriptionLatex file with one figure (eps-file). Latex file uses texdraw to generate figures that are included in the text
dc.identifierhttps://arxiv.org/abs/cond-mat/0006007
dc.identifierhttp://arxiv.org/abs/cond-mat/0006007
dc.identifierPhys.Rev.B62:12338,2000
dc.identifierdoi:10.1103/PhysRevB.62.12338
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/211834
dc.subjectStatistical Mechanics
dc.subjectHigh Energy Physics - Theory
dc.titleCritical behavior at m-axial Lifshitz points: field-theory analysis and $ε$-expansion results
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