Critical temperature shifts for finite slabs in the ε-expansion

The critical temperature Tc(b) of a d-dimensional system with finite thickness b in one of its dimensions approaches its bulk limit as b to infinity according to Tc( infinity )-Tc(b) varies as b- lambda . To first order in epsilon =4-d the shift exponent lambda is found to be given by lambda =2-((n+2)/(n+8)) epsilon +O( epsilon 2), and thus satisfies the scaling relation lambda = nu d-1, where nu d is the correlation length exponent of the bulk system and n is the order parameter dimensionality.

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

[2]  A. Bray,et al.  Surface Critical Exponents in Terms of Bulk Exponents , 1977 .

[3]  A. Bray,et al.  Critical Behavior of a Semi-infinite System:n-Vector Model in the Large-nLimit , 1977 .

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

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

[6]  P. C. Hohenberg,et al.  Surface effects on magnetic phase transitions , 1974 .

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

[8]  Shang‐keng Ma.  Introduction to the renormalization group , 1973 .

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

[10]  M. N. Barber.  Scaling Relations for Critical Exponents of Surface Properties of Magnets , 1973 .

[11]  M. Fisher,et al.  Critical phenomena in systems of finite thickness I. The spherical model , 1973 .

[12]  P. C. Hohenberg,et al.  Phase Transitions and Static Spin Correlations in Ising Models with Free Surfaces , 1972 .

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

[14]  Kenneth G. Wilson,et al.  Feynman graph expansion for critical exponents , 1972 .

[15]  M. .. Moore.  Specific heat maxima of 4He films , 1971 .

[16]  P. W. Palmberg,et al.  Surface magnetization near the critical temperature and the temperature dependence of magnetic-electron scattering from NiO , 1971 .

[17]  D. Mills.  Surface Effects in Magnetic Crystals near the Ordering Temperature , 1971 .

[18]  M. Fisher,et al.  Bounded and Inhomogeneous Ising Models. I. Specific-Heat Anomaly of a Finite Lattice , 1969 .

[19]  H. E. Stanley,et al.  Spherical Model as the Limit of Infinite Spin Dimensionality , 1968 .

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