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Scaling and nonscaling finite-size effects in the Gaussian and the mean spherical model with free boundary conditions | | X.S. Chen
; V. Dohm
; | | Date: |
16 Dec 2002 | | Subject: | cond-mat | | Abstract: | We calculate finite-size effects of the Gaussian model in a L imes ilde L^{d-1} box geometry with free boundary conditions in one direction and periodic boundary conditions in d-1 directions for 23 but logarithmic deviations from finite-size scaling are found for the free energy and energy density at the Gaussian upper borderline dimension d* =3. The logarithms are related to the vanishing critical exponent 1-alpha-
u=(d-3)/2 of the Gaussian surface energy density. The latter has a cusp-like singularity in d>3 dimensions. We show that these properties are the origin of nonscaling finite-size effects in the mean spherical model with free boundary conditions in d>=3 dimensions. At bulk T_c in d=3 dimensions we find an unexpected non-logarithmic violation of finite-size scaling for the susceptibility chi sim L^3 of the mean spherical model in film geometry whereas only a logarithmic deviation chisim L^2 ln L exists for box geometry. The result for film geometry is explained by the existence of the lower borderline dimension d_l = 3, as implied by the Mermin-Wagner theorem, that coincides with the Gaussian upper borderline dimension d*=3. For 3=T_c. | | Source: | arXiv, cond-mat/0212362 | | Services: | Forum | Review | PDF | Favorites | |
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