Biomedical subjects

V Dohm

Publications and source records attributed to V Dohm.

At least 19 recordsLinked to original sources

PubMed2004

Nonuniversal finite-size scaling in anisotropic systems.

We study the bulk and finite-size critical behavior of the O(n) symmetric phi4 theory with spatially anisotropic interactions of noncubic symmetry in d<4 dimensions. In such systems of a given (d,n) universality class, two-scale factor universality is absent in bulk correlation functions, and finite-size scaling functions including the Privman-Fisher scaling form of the free energy, the Binder cumulant ratio, and the Casimir amplitude are shown to be nonuniversal. In particular it is shown that, for anisotropic confined systems, isotropy cannot be restored by an anisotropic scale transformation.

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PubMed2003

Scaling and nonscaling finite-size effects in the Gaussian and the mean spherical model with free boundary conditions.

We calculate finite-size effects of the Gaussian model in a Lx(d-1) box geometry with free boundary conditions in one direction and periodic boundary conditions in d-1 directions for 2 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 d > or =3 dimensions. At bulk T(c), in d=3 dimensions we find an unexpected nonlogarithmic violation of finite-size scaling for the susceptibility chi approximately L3 of the mean spherical model in film geometry, whereas only a logarithmic deviation chi approximately L2 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 or =T(c).

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PubMed2003

Minimal renormalization without epsilon expansion: four-loop free energy in three dimensions for general n above and below Tc.

We present an analytic four-loop calculation of the free energy in three dimensions within the O(n) symmetric phi(4) theory at infinite cutoff for general n above and below T(c). It is shown that Goldstone singularities arising at intermediate stages of the calculation cancel among themselves. The correlation length above T(c) and an appropriately defined pseudocorrelation length below T(c) are calculated analytically up to four-loop order for general n. The method of minimal renormalization at fixed dimension d=3 is used to determine the analytic expressions for the four-loop series of the amplitude functions of the free energy, correlation length, and specific heat above and below T(c) in terms of the renormalized coupling. These expressions provide the basis for future accurate Borel resummations of universal amplitude ratios characterizing the asymptotic critical behavior and of crossover functions describing the nonasymptotic critical behavior. A brief application is given by a variational calculation of the universal specific-heat amplitude ratios A+/A- and P=alpha(-1)(1-A+/A-) and of the universal quantity R+(xi)=xi+0(A+)(1/d) for general n.

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PubMed2002

Nonuniversal size dependence of the free energy of confined systems near criticality.

The singular part of the finite-size free-energy density f(s) of the O(n) symmetric phi(4) field theory is calculated for confined geometries of linear size L with periodic boundary conditions in the large-n limit and with Dirichlet boundary conditions in one-loop order. We find that both a sharp cutoff and a subleading long-range interaction cause a leading nonuniversal L dependence of f(s) near T(c). This implies a significant restriction for the validity of universal finite-size scaling for model systems and real systems. For film geometry we predict a leading nonuniversal contribution to the critical Casimir force above the superfluid transition of (4)He.

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PubMed2000

Universality and straight phi(4) theory of finite-size effects above the upper critical dimension.

We analyze finite-size effects in a L(d) geometry above the upper critical dimension d=4 within the O(n) symmetric straight phi(4) theory on the basis of exact results for n-->infinity and one-loop results for n=1. We show that finite-size effects of the straight phi(4) continuum theory with a smooth (rather than sharp) cutoff belong to the same universality class as those of the straight phi(4) lattice theory. Our analysis predicts both universal and nonuniversal features of finite-size effects and resolves long-standing discrepancies in earlier analyses of Monte Carlo (MC) data for the d=5 Ising model. Our estimates of two fundamental length scales xi(0) and l(0) are confirmed by very recent MC data.

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PubMed1996