arXiv subjects

H. W. Diehl

Publications and source records attributed to H. W. Diehl.

49 records · Page 3Linked to original sources

arXiv1999

Field-Theoretical Analysis of Critical and Coexistence Singularities at Critical End Points

Continuum models with critical end points are considered whose Hamiltonian ${\mathcal{H}}[ϕ,ψ]$ depends on two densities $ϕ$ and $ψ$. Field-theoretic methods are used to show the equivalence of the critical behavior on the critical line and at the critical end point and to give a systematic derivation of critical-end-point singularities like the thermal singularity $\sim|{t}|^{2-α}$ of the spectator-phase boundary and the coexistence singularities $\sim |{t}|^{1-α}$ or $\sim|{t}|^β$ of the secondary density $<ψ>$. The appearance of a discontinuity eigenexponent associated with the critical end point is confirmed, and the mechanism by which it arises in field theory is clarified.

cond-mat.stat-mech↗

arXiv1998

Massive Field-Theory Approach to Surface Critical Behavior in Three-Dimensional Systems

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 $ε$ expansion. The approach is elaborated for the representative case of the semi-infinite $|\bboxϕ|^4$ $n$-vector model with a boundary term ${1/2} c_0\int_{\partial V}\bboxϕ^2$ in the action. To make the theory uv finite in bulk dimensions $3\le d<4$, 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 $m\to 0$ with $c/m\to 0$ and $c/m\to\infty$, respectively. It is shown that the surface-enhancement renormalization turns into an additive renormalization in the limit $c/m\to\infty$. 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 Padé-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 $Φ$.

cond-mat.stat-mech↗

arXiv1998

Critical behaviour of three-dimensional Ising ferromagnets at imperfect surfaces: Bounds on the surface critical exponent $β_1$

The critical behaviour of three-dimensional semi-infinite Ising ferromagnets at planar surfaces with (i) random surface-bond disorder or (ii) a terrace of monatomic height and macroscopic size is considered. The Griffiths-Kelly-Sherman correlation inequalities are shown to impose constraints on the order-parameter density at the surface, which yield upper and lower bounds for the surface critical exponent $β_1$. If the surface bonds do not exceed the threshold for supercritical enhancement of the pure system, these bounds force $β_1$ to take the value $β_1^{ord}$ of the latter system's ordinary transition. This explains the robustness of $β_1^{ord}$ to such surface imperfections observed in recent Monte Carlo simulations.

cond-mat.stat-mech↗

arXiv1998

The Theory of Boundary Critical Phenomena

An introduction into the theory of boundary critical phenomena and the application of the field-theoretical renormalization group method to these is given. The emphasis is on a discussion of surface critical behavior at bulk critical points of magnets, binary alloys, and fluids. Yet a multitude of related phenomena are mentioned. The most important distinct surface universality classes that may occur for a given universality class of bulk critical behavior are described, and the respective boundary conditions of the associated field theories are discussed. The short-distance singularities of the order-parameter profile in the diverse asymptotic regimes are surveyed.

cond-mat.stat-mech↗

arXiv1997

Surface critical behavior of bcc binary alloys

The surface critical behavior of bcc binary alloys undergoing a continuous B2-A2 order-disorder transition is investigated in the mean-field (MF) approximation. Our main aim is to provide clear evidence for the fact that surfaces which break the two-sublattice symmetry generically display the critical behavior of the NORMAL transition, whereas symmetry-preserving surfaces exhibit ORDINARY surface critical behavior. To this end we analyze the lattice MF equations for both types of surfaces in terms of nonlinear symplectic maps and derive a Ginzburg-Landau model for the symmetry-breaking (100) surface. The crucial feature of the continuum model is the emergence of an EFFECTIVE ORDERING (``staggered'') SURFACE FIELD, which depends on temperature and the other lattice model parameters, and which explains the appearance of NORMAL critical behavior for symmetry-breaking surfaces.

cond-mat.stat-mech↗

arXiv1997

Wetting phenomena in bcc binary alloys

We study the influence of the surface orientation on the wetting behavior of bcc binary alloys, using a semi-infinite lattice model equivalent to a nearest-neighbor Ising antiferromagnet in an external field. The salient feature of the model is the generation of an ``effective'' ordering surface field for symmetry-breaking surface orientations like (100). Such a field couples to the local order parameter at the surface and leads to the occurrence of wetting phenomena below the critical temperature T_c. Utilizing a Ginzburg-Landau continuum model which has been derived earlier from the lattice mean-field theory, the wetting phase diagram is calculated.

cond-mat.stat-mech↗

arXiv1997

Surface Critical Behavior of Binary Alloys and Antiferromagnets: Dependence of the Universality Class on Surface Orientation

The surface critical behavior of semi-infinite (a) binary alloys with a continuous order-disorder transition and (b) Ising antiferromagnets in the presence of a magnetic field is considered. In contrast to ferromagnets, the surface universality class of these systems depends on the orientation of the surface with respect to the crystal axes. There is ordinary and extraordinary surface critical behavior for orientations that preserve and break the two-sublattice symmetry, respectively. This is confirmed by transfer-matrix calculations for the two-dimensional antiferromagnet and other evidence.

cond-mat.stat-mech↗

arXiv1995

Dynamical Relaxation and Universal Short-Time Behavior in Finite Systems: The Renormalization Group Approach

We study how the finite-sized n-component model A with periodic boundary conditions relaxes near its bulk critical point from an initial nonequilibrium state with short-range correlations. Particular attention is paid to the universal long-time traces that the initial condition leaves. An approach based on renormalization-group improved perturbation theory in 4-epsilon space dimensions and a nonperturbative treatment of the q=0 mode of the fluctuating order-parameter field is developed. This leads to a renormalized effective stochastic equation for this mode in the background of the other q=0 modes; we explicitly derive it to one-loop order, show that it takes the expected finite-size scaling form at the fixed point, and solve it numerically. Our results confirm for general n that the amplitude of the magnetization density m(t) in the linear relaxation-time regime depends on the initial magnetization in the universal fashion originally found in our large-$n$ analysis [J.\ Stat. Phys. 73 (1993) 1]. The anomalous short-time power-law increase of m(t) also is recovered. For n=1, our results are in fair agreement with recent Monte Carlo simulations by Li, Ritschel, and Zheng [J. Phys. A 27 (1994) L837] for the three-dimensional Ising model.

cond-mat↗

arXiv1994

Dynamic surface critical behavior of systems with conserved bulk order parameter: Detailed RG analysis of the semi-infinite extensions of model B with and without nonconservative surface terms

The dynamic surface critical behavior of macroscopic systems whose dynamic bulk critical behavior is described by model $B$ is investigated. The semi-infinite extensions of bulk model $B$ introduced in a previous treatment [Phys. Rev. B 49, 2846 (1994)] and called models $B_A$ and $B_B$ are studied in detail by means of field-theoretic RG methods. The distinctive feature of these models is the presence or absence of relevant nonconservative surface terms. The earlier results on the structure of the required counterterms, the flow equations, and the representation of the surface critical exponents of dynamic quantities at the ordinary and special phase transitions in terms of static bulk and surface exponents are corroborated by means of an explicit two-loop calculation for $4-ε$ dimensions. For parameter values corresponding to a given static surface universality class, models $B_A$ and $B_B$ represent distinct dynamic surface universality classes. Differences between these manifest themselves in the behavior of scaling functions for dynamic surface susceptibilities. RG-improved perturbation theory is used to compute some of these susceptibilities to one-loop order.

cond-mat↗

arXiv1994

Long-time traces of the initial condition in relaxation phenomena near criticality

The time evolution of systems relaxing towards thermal equilibrium is examined near the critical temperature $T_c$, with special attention paid to the role of the initial value $m_i$ of the order parameter $ϕ$. To this end, the $n$-component model A for a cube of length $L$ is investigated. The common belief that all memory of $m_i$ is necessarily lost after a microscopic time span is shown to be unfounded. General arguments and the exact solution of the limit $n\to\infty$ show that $m_i$ leaves its traces in both the linear and nonlinear long-time relaxation of $ϕ$ near or at $T_c$. Specifically for linear relaxation near $T_c$, or at $T_c$ with $L<\infty$, the amplitude of the exponential decay depends on $m_i$ and the short-time exponent $θ'=(x_i-x_ϕ)/z$, provided $t_i\sim m_i^{-z/x_i}$ is comparable to or larger than other time scales. Here $x_i$ is the scaling dimension of $m_i$, $z$ is the dynamic bulk exponent, and $x_ϕ$ is the usual equilibrium scaling dimension of $ϕ$.

cond-mat↗

arXiv1994

Surface critical behavior in fixed dimensions $d<4$: Nonanalyticity of critical surface enhancement and massive field theory approach

The critical behavior of semi-infinite systems in fixed dimensions $d<4$ is investigated theoretically. The appropriate extension of Parisi's massive field theory approach is presented.Two-loop calculations and subsequent Padé-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 $Φ(d=3)$, for which we obtain the values $Φ(n=1)\simeq 0.54$ and $Φ(n=0)\simeq 0.52$, considerably lower than the previous $ε$-expansion estimates.

cond-mat↗

arXiv1994

Ordinary, extraordinary, and normal surface transitions: extraordinary-normal equivalence and simple explanation of $|T-T_c|^{2-α}$ singularities

With simple, exact arguments we show that the surface magnetization $m_1$ at the extraordinary and normal transitions and the surface energy density $ε_1$ at the ordinary, extraordinary, and normal transitions of semi-infinite $d$-dimensional Ising systems have leading thermal singularities $B_\pm |t|^{2-α}$, with the same critical exponent and amplitude ratio as the bulk free energy $f_b(t,0)$. The derivation is carried out in three steps: (i) By tracing out the surface spins, the semi-infinite Ising model with supercritical surface enhancement $g$ and vanishing surface magnetic field $h_1$ is mapped exactly onto a semi-infinite Ising model with subcritical surface enhancement, a nonzero surface field, and irrelevant additional surface interactions. This establishes the equivalence of the extraordinary ($h_1=0, g>0$) and normal ($h_1\neq 0, g<0$) transitions. (ii) The magnetization $m_1$ at the interface of an infinite system with uniform temperature $t$ and a nonzero magnetic field $h$ in the half-space $z>0$ only is shown to be proportional to $f_b(t,0)-f_b(t,h)$. (iii) The energy density $ε_1$ at the interface of an infinite system with temperatures $t_+$ and $t$ in the half-spaces $z>0$ and $z<0$ and no magnetic field is shown to be proportional to $f_b(t,0)-f_b(t_+,0)$.

cond-mat↗

arXiv1994

Universal order-parameter profiles for critical adsorption and the extraordinary transition: a comparison of epsilon-expansion and Monte Carlo results

The universal, scaled order parameter profiles $P_{\pm}(z/ξ)$ for critical adsorption of a fluid or fluid mixture onto a wall or interface, and for the extraordinary transition of the semi-infinite Ising model, are discussed theoretically, where $z$ is the distance from the interface, $ξ(T)$ is the bulk correlation length, and the subscript $+$ ($-$) refers to the approach from above (below) $T_c$. Recent results to first order in the $ε=4-d$ expansion are extrapolated to $d=3$ space dimensions and compared with new Monte Carlo results. In order to obtain meaningful extrapolations it is crucial that both the exponential decay at large $ζ$ as well as the known algebraic behavior $P_{\pm}(ζ)\simζ^{-β/ν}$ at small $ζ$ be correctly reproduced. To this end a recently developed novel RG scheme involving a $z$ dependent amplitude renormalization is used. Reasonable agreement of our extrapolations with the Monte Carlo results and some experimental results is obtained.

cond-mat↗