Knowledge Management System of Institute of Theoretical Physics, CAS
Chen, XS; Dohm, V; Chen, XS , Chinese Acad Sci, Inst Theoret Phys, POB 2735, Beijing 100080, Peoples R China. | |
Scaling and nonscaling finite-size effects in the Gaussian and the mean spherical model with free boundary conditions | |
Source Publication | PHYSICAL REVIEW E |
Keyword | Upper Critical Dimension T-lambda Confined He-4 Free-energy Superfluid Transition Critical-behavior Phi(4) Theory 3 Dimensions Heat Systems |
Abstract | We calculate finite-size effects of the Gaussian model in a LxL(d-1) box geometry with free boundary conditions in one direction and periodic boundary conditions in d-1 directions for 2<4. We also consider film geometry (L-->infinity). Finite-size scaling is found to be valid for d<3 and d>3 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-nu=(d-3)/2 of the Gaussian surface energy density. The latter has a cusplike 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 dgreater than or equal to3 dimensions. At bulk T(c), in d=3 dimensions we find an unexpected nonlogarithmic violation of finite-size scaling for the susceptibility chisimilar toL(3) of the mean spherical model in film geometry, whereas only a logarithmic deviation chisimilar toL(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<4 we find a power-law violation of scaling chisimilar toL(d-1) at bulk T(c) for box geometry and a nonscaling temperature dependence chi(surface)similar toxi(d) of the surface susceptibility above T(c). For 2<3 dimensions we show the validity of universal finite-size scaling for the susceptibility of the mean spherical model with free boundary conditions for both box and film geometry and calculate the corresponding universal scaling functions for Tgreater than or equal toT(c). |
2003 | |
ISSN | 1539-3755 |
Volume | 67Issue:5Pages:- |
Subject Area | Physics |
Indexed By | SCI |
Citation statistics | |
Document Type | 期刊论文 |
Identifier | http://ir.itp.ac.cn/handle/311006/13313 |
Collection | 理论物理所科研产出_SCI论文 |
Corresponding Author | Chen, XS , Chinese Acad Sci, Inst Theoret Phys, POB 2735, Beijing 100080, Peoples R China. |
Recommended Citation GB/T 7714 | Chen, XS,Dohm, V,Chen, XS , Chinese Acad Sci, Inst Theoret Phys, POB 2735, Beijing 100080, Peoples R China.. Scaling and nonscaling finite-size effects in the Gaussian and the mean spherical model with free boundary conditions[J]. PHYSICAL REVIEW E,2003,67(5):-. |
APA | Chen, XS,Dohm, V,&Chen, XS , Chinese Acad Sci, Inst Theoret Phys, POB 2735, Beijing 100080, Peoples R China..(2003).Scaling and nonscaling finite-size effects in the Gaussian and the mean spherical model with free boundary conditions.PHYSICAL REVIEW E,67(5),-. |
MLA | Chen, XS,et al."Scaling and nonscaling finite-size effects in the Gaussian and the mean spherical model with free boundary conditions".PHYSICAL REVIEW E 67.5(2003):-. |
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