Lifshitz-point correlation length exponents from the large-n expansion |
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Authors: | MA Shpot YuM Pisʼmak |
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Institution: | 1. Institute for Condensed Matter Physics, 79011 Lviv, Ukraine;2. Fakultät für Physik, Universität Duisburg-Essen, 47048 Duisburg, Federal Republic of Germany;3. State University of Sankt-Petersburg, 198504 Sankt-Petersburg, Russia |
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Abstract: | 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 νL2 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?=4+m/2 for generic m∈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. |
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Keywords: | Field theory Critical behavior Lifshitz point Large-n expansion |
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