Lifshitz-point correlation length exponents from the large-\(n\) expansion. (English) Zbl 1246.81183
Summary: The large-\(n\) expansion is applied to the calculation of thermal critical exponents describing the critical behavior of spatially anisotropic \(d\)-dimensional systems at \(m\)-axial Lifshitz points. We derive the leading non-trivial \(1/n\) correction for the perpendicular correlation-length exponent \(\nu_{L2}\) and hence several related thermal exponents to order \(O(1/n)\). The results are consistent with known large-n expansions for \(d\)-dimensional critical points and isotropic Lifshitz points, as well as with the second-order epsilon expansion about the upper critical dimension \(d^{\ast}=4+m/2\) for generic \(m\in [0,d]\). Analytical results are given for the special case \(d=4\), \(m=1\). For uniaxial Lifshitz points in three dimensions, \(1/n\) coefficients are calculated numerically. The estimates of critical exponents at \(d=3\), \(m=1\) and \(n=3\) are discussed.
MSC:
| 81T28 | Thermal quantum field theory |
| 82B27 | Critical phenomena in equilibrium statistical mechanics |
| 35B33 | Critical exponents in context of PDEs |
Software:
MathematicaReferences:
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