Critical phenomena at interfaces

Equilibrium aspects of the structure and thermodynamics of the interfacial region separating two coexisting phases near criticality are reviewed. Brief surveys of pertinent rigorous and exact results and experiments are included. Phenomenological approaches and renormalisation group results, along with implications on such topics as universality and interface stability, are discussed. Related topics such as roughening and wetting are also briefly discussed.

[1]  D. Nelson,et al.  Equations of state and renormalization-group recursion relations , 1976 .

[2]  A. Bray,et al.  Critical behaviour of semi-infinite systems , 1977 .

[3]  F. David INFRARED DIVERGENCES OF MEMBRANE MODELS , 1981 .

[4]  R. Bausch Ginzburg criterion for tricritical points , 1972 .

[5]  The liquid–vapor interface of a binary liquid mixture , 1981 .

[6]  C. Bervillier Universal relations among critical amplitude. Calculations up to order epsilon2 for systems with continuous symmetry , 1976 .

[7]  P. G. de Gennes,et al.  Some effects of long range forces on interfacial phenomena , 1981 .

[8]  F. Ramos-Gómez Interfacial tensions and susceptibilities in a model three‐phase system , 1981 .

[9]  L. Kadanoff Scaling laws for Ising models near T(c) , 1966 .

[10]  J. Lebowitz,et al.  On the local structure of the phase separation line in the two-dimensional Ising system , 1981 .

[11]  R. Hocken,et al.  Ising critical exponents in real fluids: An experiment , 1976 .

[12]  J. Niez,et al.  Phase transition in a domain wall , 1979 .

[13]  D. E. Sullivan Surface tension and contact angle of a liquid–solid interface , 1981 .

[14]  D. Beaglehole Ellipsometric study of the surface of simple liquids , 1980 .

[15]  R. Jackiw Quantum Meaning of Classical Field Theory , 1977 .

[16]  D. Nelson,et al.  Equations of State for Tricritical Points , 1975 .

[17]  John W. Cahn,et al.  Critical point wetting , 1977 .

[18]  Michael E. Fisher,et al.  Theory of Critical-Point Scattering and Correlations. I. The Ising Model , 1967 .

[19]  The transfer matrix for a pure phase in the two-dimensional Ising model , 1973 .

[20]  J. Gervais,et al.  Extended Particles in Quantum Field Theories , 1975 .

[21]  T. Lubensky,et al.  εExpansion in Semi-infinite Ising Systems , 1973 .

[22]  R. Griffiths Thermodynamic model for tricritical points in ternary and quaternary fluid mixtures , 1974 .

[23]  W. Webb,et al.  Critical Liquid-Vapor Interface in S F 6 . I. Thickness of the Diffuse Transition Layer , 1973 .

[24]  Michael Aizenman,et al.  Translation invariance and instability of phase coexistence in the two dimensional Ising system , 1980 .

[25]  C. Franck,et al.  New Critical Anomaly Induced in a Binary Liquid Mixture by a Selectively Adsorbing Wall , 1982 .

[26]  K. Kawasaki,et al.  An exact solution of the renormalization-group equations for the mean field theory of stable and metastable states , 1981 .

[27]  J. Kosterlitz,et al.  The critical properties of the two-dimensional xy model , 1974 .

[28]  Michael E. Fisher,et al.  The renormalization group in the theory of critical behavior , 1974 .

[29]  P. Leiderer,et al.  Interfacial tension near the tricritical point in3He-4He mixtures , 1977 .

[30]  H. Wagner Long-wavelength excitations and the Goldstone theorem in many-particle systems with “broken symmetries” , 1966 .

[31]  R. Joseph,et al.  Scaled Equation of State and Critical Exponents in Magnets and Fluids , 1970 .

[32]  J. M. J. van Leeuwen,et al.  Real-Space Renormalization , 1982 .

[33]  W. Webb,et al.  Diffuse Interface in a Critical Fluid Mixture , 1965 .

[34]  J. Meunier,et al.  Optical reflectivity of a diffuse interface , 1982 .

[35]  C. Wilson Surface magnetisation profile in the critical region by the epsilon -expansion , 1980 .

[36]  M. Jhon,et al.  The origin of surface waves , 1978 .

[37]  Michael E. Fisher,et al.  Interfacial, Boundary, and Size Effects at Critical Points , 1967 .

[38]  Michael E. Fisher,et al.  Scaling Theory for Finite-Size Effects in the Critical Region , 1972 .

[39]  B. Pant,et al.  Critical domain-wall properties in weakly anisotropic systems , 1984 .

[40]  J. Lebowitz,et al.  Surface tension, percolation, and roughening , 1982 .

[41]  A. Martin-Löf,et al.  Surface tension in the Ising model , 1972 .

[42]  David Ruelle,et al.  Observables at infinity and states with short range correlations in statistical mechanics , 1969 .

[43]  Jean Zinn-Justin,et al.  Critical Exponents for the N Vector Model in Three-Dimensions from Field Theory , 1977 .

[44]  B. Widom,et al.  Noncritical interface near a critical end point II , 1980 .

[45]  J. Lebowitz,et al.  Surface tension and phase coexistence , 1981 .

[46]  S. Dietrich,et al.  Multicritical behaviour at surfaces , 1983 .

[47]  M. Fisher,et al.  Helicity Modulus, Superfluidity, and Scaling in Isotropic Systems , 1973 .

[48]  Membrabe models and generalized Z2 gauge theories , 1980 .

[49]  T. Lubensky,et al.  Critical phenomena in semi-infinite systems. I.εexpansion for positive extrapolation length , 1975 .

[50]  M. Kac On the Partition Function of a One‐Dimensional Gas , 1959 .

[51]  Jorge V. José,et al.  Renormalization, vortices, and symmetry-breaking perturbations in the two-dimensional planar model , 1977 .

[52]  J. Zittartz Microscopic Approach to Interfacial Structure in Ising-like Ferromagnets , 1967 .

[53]  Victor Martin-Mayor,et al.  Field Theory, the Renormalization Group and Critical Phenomena , 1984 .

[54]  D. Beaglehole Adsorption at the liquid–vapor interface of a binary liquid mixture , 1980 .

[55]  J. Kestin,et al.  The viscocity of carbon dioxide in the neighbourhood of the critical point , 1964 .

[56]  E. Olivieri,et al.  Non-translation invariant Gibbs states with coexisting phases , 1979 .

[57]  J. Weeks,et al.  Pinning and roughening of one-dimensional models of interfaces and steps , 1981 .

[58]  J. Zinn-Justin,et al.  Phase transitions : Cargèse 1980 , 1982 .

[59]  D. J. Wallace,et al.  Instantons and the Ising model below Tc , 1980 .

[60]  S. Leibler,et al.  Observation of an anomalous adsorption in a critical binary mixture , 1982 .

[61]  S. Leibler,et al.  Critical Wetting in Three Dimensions , 1983 .

[62]  W. J. Camp,et al.  Behavior of Two-Point Correlation Functions Near and on a Phase Boundary , 1971 .

[63]  Y. Goldschmidt,et al.  Surface energy and specific heat for a semi-infinite medium , 1984 .

[64]  J. Rudnick,et al.  epsilon expansion for the interfacial profile , 1978 .

[65]  D. Beaglehole Short-ranged roughness on the near-critical liquid interface , 1982 .

[66]  D. E. Aspnes,et al.  Static Phenomena Near Critical Points: Theory and Experiment , 1967 .

[67]  Diffuse Interface in a Critical Fluid Mixture , 1969 .

[68]  K. Symanzik SCHRODINGER REPRESENTATION AND CASIMIR EFFECT IN RENORMALIZABLE QUANTUM FIELD THEORY , 1981 .

[69]  J. Langevin Cent ans de Journal de Physique , 1972 .

[70]  J. Meunier,et al.  Étude spectrale de la lumière diffusée par les fluctuations thermiques de l'interface liquide vapeur de CO2 près de son point critique. mesure de la tension superficielle et de la viscosité , 1974 .

[71]  D. Thouless,et al.  Ordering, metastability and phase transitions in two-dimensional systems , 1973 .

[72]  M. Bouchiat,et al.  Spectre des fluctuations thermiques de la surface libre d'un liquide simple , 1971 .

[73]  M. J. Stephen Tricritical points in nonsymmetric systems , 1975 .

[74]  H. Horner,et al.  Goldstone mode singularities and equation of state of an isotropic magnet , 1978 .

[75]  C. Eckart The Penetration of a Potential Barrier by Electrons , 1930 .

[76]  B. Widom Structure of the αγ interface , 1978 .

[77]  J. Weeks Structure and thermodynamics of the liquid–vapor interface , 1977 .

[78]  P. Hohenberg Surface tension anomaly at the superfluid transition , 1973 .

[79]  R. L. Dobrushin,et al.  Gibbs State Describing Coexistence of Phases for a Three-Dimensional Ising Model , 1973 .

[80]  R. Pandit,et al.  Surfaces and interfaces of lattice models: mean-field theory as an area-preserving map , 1982 .

[81]  P. G. Watson LETTERS TO THE EDITOR: Critical behaviour of boundary susceptibility and boundary tension , 1968 .

[82]  L. Onsager Crystal statistics. I. A two-dimensional model with an order-disorder transition , 1944 .

[83]  R. Griffiths,et al.  Thermodynamic model for tricritical mixtures with application to ammonium sulfate + water + ethanol + benzene , 1982 .

[84]  K. Kawasaki,et al.  Renormalization Group Approach to the Interfacial Order Parameter Profile near the Critical Point , 1977 .

[85]  T. Burkhardt,et al.  Renormalization-group approach to the Ising model with a free surface , 1977 .

[86]  J. Lebowitz,et al.  Statistical Thermodynamics of Nonuniform Fluids , 1963 .

[87]  S. Dietrich,et al.  Field-theoretical approach to multicritical behavior near free surfaces , 1981 .

[88]  G. A. Baker CERTAIN GENERAL ORDER-DISORDER MODELS IN THE LIMIT OF LONG-RANGE INTERACTIONS , 1962 .

[89]  G. Gallavotti The phase separation line in the two-dimensional Ising model , 1972 .

[90]  James S. Langer,et al.  Theory of the condensation point , 1967 .

[91]  S. Leibler,et al.  Critical adsorption: The renormalization-group approach , 1983 .

[92]  B. U. Felderhof Dynamics of the diffuse gas-liquid interface near the critical point , 1970 .

[93]  J. Cahn,et al.  Thickness of the Liquid-Vapor Wetting Layer , 1982 .

[94]  T. Lubensky,et al.  Critical phenomena in semi-infinite systems. II. Mean-field theory , 1975 .

[95]  B. Widom,et al.  Interfacial tensions in a system of three liquid phases , 1976 .

[96]  D. Pohl,et al.  Wetting Transition in Lutidine-Water Mixtures , 1982 .

[97]  D. Stauffer,et al.  Universality of Second-Order Phase Transitions: The Scale Factor for the Correlation Length , 1972 .

[98]  D. Nelson Coexistence-curve singularities in isotropic ferromagnets , 1976 .

[99]  A. Messager,et al.  Correlation functions and boundary conditions in the ising ferromagnet , 1977 .

[100]  S. Leibler,et al.  Critical wetting : the domain of validity of mean field theory , 1983 .

[101]  J. Rudnick,et al.  Order-Parameter Profile in Semi-Infinite Systems at Criticality , 1982 .

[102]  M. T. D. Gama,et al.  Adsorption and wetting transitions at a model of the interface between a solid and a binary fluid mixture , 1983 .

[103]  W. Goldburg,et al.  Test of mean‐field behavior by light scattering in three phases of a fluid mixture near its tricritical point , 1979 .

[104]  J. R. Schrieffer,et al.  Dynamics and statistical mechanics of a one-dimensional model Hamiltonian for structural phase transitions , 1974 .

[105]  J. Weeks,et al.  Structural Transition in the Ising-Model Interface , 1973 .

[106]  S. C. Greer Coexistence curves at liquid-liquid critical points: Ising exponents and extended scaling , 1976 .

[107]  S. Dietrich,et al.  Critical behaviour of the energy density in semi-infinite systems , 1981 .

[108]  L. Peliti,et al.  Magnetisation profile in the presence of a surface magnetic field , 1982 .

[109]  B. Widom,et al.  Liquid-vapor surface tension near the liquid-liquid consolute point , 1980 .

[110]  P. Hohenberg,et al.  Theory of Dynamic Critical Phenomena , 1977 .

[111]  D. J. Wallace,et al.  Droplet Theory of Low-Dimensional Ising Models , 1981 .

[112]  B. Widom,et al.  Surface Tension and Molecular Correlations near the Critical Point , 1965 .

[113]  J. Weeks,et al.  Agreement of Capillary-Wave Theory with Exact Results for the Interface Profile of the Two-Dimensional Ising Model , 1982 .

[114]  D. Landau,et al.  Fluctuation-induced first-order transition in a bcc Ising model with competing interactions , 1979 .

[115]  C. Knobler,et al.  Experimental studies of nucleation in near‐critical liquid mixtures , 1980 .

[116]  T. M. Sanders,et al.  Surface Tension of He 4 near T λ , 1976 .

[117]  M. Lowe,et al.  Domain wall singularity in a Landau-Ginzburg model , 1981 .

[118]  John S. Rowlinson,et al.  New Model for the Study of Liquid–Vapor Phase Transitions , 1970 .

[119]  B. Widom,et al.  Structure and Free Energy of the Interface between Fluid Phases in Equilibrium near the Critical Point , 1969 .

[120]  D. Abraham Capillary Waves and Surface Tension: An Exactly Solvable Model , 1981 .

[121]  D. Abraham Intrinsic structure and long-ranged correlations in interfaces , 1984 .

[122]  Kurt Binder,et al.  Monte Carlo calculation of the surface tension for two- and three-dimensional lattice-gas models , 1982 .

[123]  D. Grempel,et al.  Singularities of the surface magnetisation profile near the critical point , 1980 .

[124]  Jacques Meunier,et al.  Diffusion de la lumière par les ondes de surface sur CO2 près du point critique mesure de la tension superficielle , 1969 .

[125]  R. Evans The role of capillary wave fluctuations in determining the liquid-vapour interface , 1981 .

[126]  J. Rudnick,et al.  Interfacial Profile in Three Dimensions , 1978 .

[127]  K. Kawasaki,et al.  Renormalization Group Theory of the Interfacial Roughening Transition , 1978 .

[128]  D. Abraham,et al.  Interface profile of the Ising ferromagnet in two dimensions , 1976 .

[129]  A. Martin-Löf,et al.  Surface tension in the two-dimensional Ising model , 1973 .

[130]  Jean-Pierre Hansen,et al.  Phase Transitions of the Lennard-Jones System , 1969 .

[131]  D. Abraham Solvable Model with a Roughening Transition for a Planar Ising Ferromagnet , 1980 .

[132]  W. Webb,et al.  Critical Liquid-Vapor Interface in SF6. II. Thermal Excitations, Surface Tension, and Viscosity , 1973 .

[133]  R. Griffiths,et al.  Ising-Model Surface Tension Using Real-Space Renormalization-Group Methods , 1978 .

[134]  A. Bray,et al.  Experimental Determination of the Critical Correlation Function for a Binary Liquid Mixture: Evidence for Universality , 1976 .

[135]  D. J. Wallace,et al.  Euclidean group as a dynamical symmetry of surface fluctuations: The planar interface and critical behavior , 1979 .

[136]  J. Langer,et al.  Dynamics of a diffuse liquid-vapor interface , 1980 .

[137]  D. Forster,et al.  Critical behavior of an e-dimensional planar interface , 1981 .

[138]  H. Burstyn,et al.  Correlation function near the critical mixing point of a binary liquid , 1979 .

[139]  J. Rudnick,et al.  Erratum: Renormalization-group proof of Josephson's relation andεexpansion for the helicity modulus (superfluid density) , 1977 .

[140]  M. .. Moore,et al.  Spin-Spin Correlation Function of the Three-Dimensional Ising Ferromagnet Above the Curie Temperature , 1969 .

[141]  Farid F. Abraham,et al.  On the thermodynamics, structure and phase stability of the nonuniform fluid state , 1979 .

[142]  F. Stillinger,et al.  Interfacial Density Profile for Fluids in the Critical Region , 1965 .

[143]  M. Schick,et al.  Continuous and first-order wetting transition from the van der Waals theory of fluids , 1983 .

[144]  J. L. Lebowitz,et al.  ON THE SURFACE TENSION OF LATTICE SYSTEMS * , 1980 .

[145]  D. M. Kroll,et al.  The interface in a Ginsburg-Landau-Wilson model: Derivation of the drumhead model in the low-temperature limit , 1980 .

[146]  D. Meiron,et al.  Ising Model Critical Indices in Three-Dimensions from the Callan-Symanzik Equation , 1976 .

[147]  Shang‐keng Ma Modern Theory of Critical Phenomena , 1976 .

[148]  B. Widom Antonoff's Rule and the Structure of Interfaces near Tricritical Points , 1975 .

[149]  T. Burkhardt Localisation-delocalisation transition in a solid-on-solid model with a pinning potential , 1981 .

[150]  N. Svrakic,et al.  Renormalization-group calculation of the critical properties of a free magnetic surface , 1977 .

[151]  Michael E. Fisher,et al.  The theory of condensation and the critical point , 1967 .

[152]  J. Straley,et al.  Logarithmic corrections to the mean-field theory of tricritical points , 1975 .

[153]  J. Rudnick First-order transition induced by cubic anisotropy , 1978 .

[154]  W. Webb,et al.  Interfacial Tension of Near‐Critical Cyclohexane–Methanol Mixtures , 1969 .

[155]  J. Gunton,et al.  Renormalization group in critical phenomena and quantum field theory : proceedings of a conference,Temple University, May 29-31, 1973 , 1973 .

[156]  G. Joyce Spherical Model with Long-Range Ferromagnetic Interactions , 1966 .

[157]  B. Widom,et al.  Equation of State in the Neighborhood of the Critical Point , 1965 .

[158]  M. Fisher,et al.  Multicriticality of Wetting, Prewetting, and Surface Transitions , 1982 .

[159]  M. Fisher The theory of equilibrium critical phenomena , 1967 .

[160]  H. Temperley Statistical mechanics and the partition of numbers II. The form of crystal surfaces , 1952, Mathematical Proceedings of the Cambridge Philosophical Society.

[161]  E. Tomboulis Canonical quantization of nonlinear waves , 1975 .

[162]  Interfacial tensions of three fluid phases in equilibrium , 1975 .

[163]  M. Fisher Critical Phenomena in Films and Surfaces , 1973 .

[164]  T. D. Lee,et al.  Statistical Theory of Equations of State and Phase Transitions. II. Lattice Gas and Ising Model , 1952 .

[165]  J. E. Hilliard,et al.  Free Energy of a Nonuniform System. I. Interfacial Free Energy , 1958 .

[166]  J. Weeks,et al.  Phase transition in the two-dimensional Coulomb gas, and the interfacial roughening transition , 1976 .

[167]  W. Goldburg,et al.  Light Scattering and Sum Rules in Three Phases of a Liquid Mixture near Its Tricritical Point , 1980 .

[168]  D. Stroud,et al.  Density-functional theory of simple classical fluids. I. Surfaces , 1976 .

[169]  H. Beijeren Interface sharpness in the Ising system , 1975 .

[170]  D. J. Wallace,et al.  Goldstone modes in vacuum decay and first-order phase transitions , 1980 .

[171]  M. Fisher,et al.  Theory of critical point scattering and correlations. III. The Ising model below T c and in a field , 1975 .

[172]  J. Hubbard Critical behaviour of the Ising model , 1972 .

[173]  W. Selke,et al.  Interface properties of the three-state potts model in two dimensions , 1982 .

[174]  J. Zollweg,et al.  Surface Tension and Viscosity of Xenon Near Its Critical Point , 1971 .

[175]  M. Fisher,et al.  Critical wall perturbations and a local free energy functional , 1980 .

[176]  L. Kadanoff Notes on Migdal's recursion formulas , 1976 .

[177]  J. Zittartz,et al.  Interface free energy and transition temperature of the square-lattice Ising antiferromagnet at finite magnetic field , 1977 .

[178]  J. Dufty,et al.  Quantum fluids and solids , 1977 .

[179]  Mark Kac,et al.  The Spherical Model of a Ferromagnet , 1952 .

[180]  B. Widom Noncritical interface near a critical end point , 1977 .

[181]  P. Pincus,et al.  Surface spinodals and extended wetting in fluids and polymer solutions , 1983 .

[182]  P. Wiegmann One-dimensional Fermi system and plane xy model , 1978 .

[183]  J. Cahn,et al.  An Interface Phase Transition: Complete to Partial Wetting , 1980, Science.

[184]  P. Hohenberg,et al.  Two-scale-factor universality and the renormalization group , 1976 .