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Register a new userSurface critical behavior in fixed dimensions $d<4$: Nonanalyticity of critical surface enhancement and massive field theory approach
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Hans Werner Diehl Phy300
Publication date
1994
fields
Physics
and research's language is
English
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The critical behavior of semi-infinite systems in fixed dimensions $d<4$ is investigated theoretically. The appropriate extension of Parisis massive field theory approach is presented.Two-loop calculations and subsequent Pade-Borel analyses of surface critical exponents of the special and ordinary phase transitions yield estimates in reasonable agreement with recent Monte Carlo results. This includes the crossover exponent $Phi (d=3)$, for which we obtain the values $Phi (n=1)simeq 0.54$ and $Phi (n=0)simeq 0.52$, considerably lower than the previous $epsilon$-expansion estimates.
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The massive field-theory approach for studying critical behavior in fixed space dimensions $d<4$ is extended to systems with surfaces.This enables one to study surface critical behavior directly in dimensions $d<4$ without having to resort to the $epsilon$ expansion. The approach is elaborated for the representative case of the semi-infinite $|bbox{phi}|^4$ $n$-vector model with a boundary term ${1/2} c_0int_{partial V}bbox{phi}^2$ in the action. To make the theory uv finite in bulk dimensions $3le d<4$, a renormalization of the surface enhancement $c_0$ is required in addition to the standard mass renormalization. Adequate normalization conditions for the renormalized theory are given. This theory involves two mass parameter: the usual bulk `mass (inverse correlation length) $m$, and the renormalized surface enhancement $c$. Thus the surface renormalization factors depend on the renormalized coupling constant $u$ and the ratio $c/m$. The special and ordinary surface transitions correspond to the limits $mto 0$ with $c/mto 0$ and $c/mtoinfty$, respectively. It is shown that the surface-enhancement renormalization turns into an additive renormalization in the limit $c/mtoinfty$. The renormalization factors and exponent functions with $c/m=0$ and $c/m=infty$ that are needed to determine the surface critical exponents of the special and ordinary transitions are calculated to two-loop order. The associated series expansions are analyzed by Pade-Borel summation techniques. The resulting numerical estimates for the surface critical exponents are in good agreement with recent Monte Carlo simulations. This also holds for the surface crossover exponent $Phi$.
The dynamic critical behavior of isotropic Heisenberg ferromagnets with a planar free surface is investigated by means of field-theoretic renormalization group techniques and high-precision computer simulations. An appropriate semi-infinite extension of the stochastic model J is constructed. The relevant boundary terms of the action of the associated dynamic field theory are identified, the implied boundary conditions are derived, and the renormalization of the model in $d<6$ bulk dimensions is clarified. Two distinct renormalization schemes are utilized. The first is a massless one based on minimal subtraction of dimensional poles and the dimensionality expansion about $d=6$. To overcome its problems in going below $d=4$ dimensions, a massive one for fixed dimensions $dle 4$ is constructed. The resulting renormalization group (or Callan Symanzik) equations are exploited to obtain the scaling forms of surface quantities like the dynamic structure factor. In conjunction with boundary operator expansions scaling relations follow that relate the critical indices of the dynamic and static infrared singularities of surface quantities to familiar emph{static} bulk and surface exponents. To test the predicted scaling forms and scaling-law expressions for the critical exponents involved, accurate computer-simulation data are presented for the dynamic surface structure factor. These are in conformity with our predictions.
We consider semi-infinite two-dimensional layered Ising models in the extreme anisotropic limit with an aperiodic modulation of the couplings. Using substitution rules to generate the aperiodic sequences, we derive functional equations for the surface magnetization. These equations are solved by iteration and the surface magnetic exponent can be determined exactly. The method is applied to three specific aperiodic sequences, which represent different types of perturbation, according to a relevance-irrelevance criterion. On the Thue-Morse lattice, for which the modulation is an irrelevant perturbation, the surface magnetization vanishes with a square root singularity, like in the homogeneous lattice. For the period-doubling sequence, the perturbation is marginal and the surface magnetic exponent varies continuously with the modulation amplitude. Finally, the Rudin-Shapiro sequence, which corresponds to the relevant case, displays an anomalous surface critical behavior which is analyzed via scaling considerations: Depending on the value of the modulation, the surface magnetization either vanishes with an essential singularity or remains finite at the bulk critical point, i.e., the surface phase transition is of first order.
We report measurements of the de Haas-van Alphen effect in CeIn3 in magnetic fields extending to ~90 T, well above the Neel critical field of Hc ~61 T. The unreconstructed Fermi surface a-sheet is observed in the high magnetic field polarized paramagnetic limit, but with its effective mass and Fermi surface volume strongly reduced in size compared to that observed in the low magnetic field paramagnetic regime under pressure. The spheroidal topology of this sheet provides an ideal realization of the transformation from a `large Fermi surface accommodating f-electrons to a `small Fermi surface when the f-electron moments become polarized.
Surface critical phenomena and the related onset of Goldstone modes probe the fundamental properties of the confining flux in Quantum Chromodynamics. New ideas on surface roughening and their implications for lattice studies of quark confinement are presented. Problems with the oversimplified string description of the Wilson flux sheet are discussed.
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