16 research outputs found
Precise determination of critical exponents and equation of state by field theory methods
Renormalization group, and in particular its Quantum Field Theory
implementation has provided us with essential tools for the description of the
phase transitions and critical phenomena beyond mean field theory. We therefore
review the methods, based on renormalized phi^4_3 quantum field theory and
renormalization group, which have led to a precise determination of critical
exponents of the N-vector model (R. Guida and J. Zinn-Justin, J. Phys. A31
(1998) 8103. cond-mat/9803240). and of the equation of state of the 3D Ising
model (R. Guida and J. Zinn-Justin, Nucl. Phys. B489 [FS] (1997) 626,
hep-th/9610223.). These results are among the most precise available probing
field theory in a non-perturbative regime.Comment: 23 pages, tex, private macros, one figur
Application of Minimal Subtraction Renormalization to Crossover Behavior near the He Liquid-Vapor Critical Point
Parametric expressions are used to calculate the isothermal susceptibility,
specific heat, order parameter, and correlation length along the critical
isochore and coexistence curve from the asymptotic region to crossover region.
These expressions are based on the minimal-subtraction renormalization scheme
within the model. Using two adjustable parameters in these
expressions, we fit the theory globally to recently obtained experimental
measurements of isothermal susceptibility and specific heat along the critical
isochore and coexistence curve, and early measurements of coexistence curve and
light scattering intensity along the critical isochore of He near its
liquid-vapor critical point. The theory provides good agreement with these
experimental measurements within the reduced temperature range
Surface critical behavior in fixed dimensions : Nonanalyticity of critical surface enhancement and massive field theory approach
The critical behavior of semi-infinite systems in fixed dimensions is
investigated theoretically. The appropriate extension of Parisi's massive field
theory approach is presented.Two-loop calculations and subsequent Pad\'e-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 , for which we obtain
the values and , considerably
lower than the previous -expansion estimates.Comment: Latex with Revtex-Stylefiles, 4 page
Effective potential in three-dimensional O(N) models
We consider the effective potential in three-dimensional models with O(N)
symmetry. For generic values of N, and in particular for the physically
interesting cases N=0,1,2,3, we determine the six-point and eight-point
renormalized coupling constants which parametrize its small-field expansion.
These estimates are obtained from the analysis of their -expansion,
taking into account the exact results in one and zero dimensions, and, for the
Ising model (i.e. N=1), the accurate high-temperature estimates in two
dimensions. They are compared with the available results from other approaches.
We also obtain corresponding estimates for the two-dimensional O() models.Comment: 22 pages, revtex, 2 fig
Crossover scaling from classical to nonclassical critical behavior
We study the crossover between classical and nonclassical critical behaviors.
The critical crossover limit is driven by the Ginzburg number G. The
corresponding scaling functions are universal with respect to any possible
microscopic mechanism which can vary G, such as changing the range or the
strength of the interactions. The critical crossover describes the unique flow
from the unstable Gaussian to the stable nonclassical fixed point. The scaling
functions are related to the continuum renormalization-group functions. We show
these features explicitly in the large-N limit of the O(N) phi^4 model. We also
show that the effective susceptibility exponent is nonmonotonic in the
low-temperature phase of the three-dimensional Ising model.Comment: 5 pages, final version to appear in Phys. Rev.
Minimal renormalization without \epsilon-expansion: Three-loop amplitude functions of the O(n) symmetric \phi^4 model in three dimensions below T_c
We present an analytic three-loop calculation for thermodynamic quantities of
the O(n) symmetric \phi^4 theory below T_c within the minimal subtraction
scheme at fixed dimension d=3. Goldstone singularities arising at an
intermediate stage in the calculation of O(n) symmetric quantities cancel among
themselves leaving a finite result in the limit of zero external field. From
the free energy we calculate the three-loop terms of the amplitude functions
f_phi, F+ and F- of the order parameter and the specific heat above and below
T_c, respectively, without using the \epsilon=4-d expansion. A Borel
resummation for the case n=2 yields resummed amplitude functions f_phi and F-
that are slightly larger than the one-loop results. Accurate knowledge of these
functions is needed for testing the renormalization-group prediction of
critical-point universality along the \lambda-line of superfluid He(4).
Combining the three-loop result for F- with a recent five-loop calculation of
the additive renormalization constant of the specific heat yields excellent
agreement between the calculated and measured universal amplitude ratio A+/A-
of the specific heat of He(4). In addition we use our result for f_phi to
calculate the universal combination R_C of the amplitudes of the order
parameter, the susceptibility and the specific heat for n=2 and n=3. Our
Borel-resummed three-loop result for R_C is significantly more accurate than
the previous result obtained from the \epsilon-expansion up to O(\epsilon^2).Comment: 29 pages LaTeX including 3 PostScript figures, to appear in Nucl.
Phys. B [FS] (1998
Minimal renormalization without epsilon-expansion: Amplitude functions in three dimensions below T_c
Massive field theory at fixed dimension d<4 is combined with the minimal
subtraction scheme to calculate the amplitude functions of thermodynamic
quantities for the O(n) symmetric phi^4 model below T_c in two-loop order.
Goldstone singularities arising at an intermediate stage in the calculation of
O(n) symmetric quantities are shown to cancel among themselves leaving a finite
result in the limit of zero external field. From the free energy we calculate
the amplitude functions in zero field for the order parameter, specific heat
and helicity modulus (superfluid density) in three dimensions. We also
calculate the q^2 part of the inverse of the wavenumber-dependent transverse
susceptibility chi_T(q) which provides an independent check of our result for
the helicity modulus. The two-loop contributions to the superfluid density and
specific heat below T_c turn out to be comparable in magnitude to the one-loop
contributions, indicating the necessity of higher-order calculations and
Pade-Borel type resummations.Comment: 41 pages, LaTeX, 8 PostScript figures, submitted to NPB [FS
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 is extended to systems with surfaces.This enables one to
study surface critical behavior directly in dimensions without having to
resort to the expansion. The approach is elaborated for the
representative case of the semi-infinite |\bbox{\phi}|^4 -vector model
with a boundary term {1/2} c_0\int_{\partial V}\bbox{\phi}^2 in the action.
To make the theory uv finite in bulk dimensions , a renormalization
of the surface enhancement 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) , and the renormalized surface enhancement .
Thus the surface renormalization factors depend on the renormalized coupling
constant and the ratio . The special and ordinary surface transitions
correspond to the limits with and ,
respectively. It is shown that the surface-enhancement renormalization turns
into an additive renormalization in the limit . The
renormalization factors and exponent functions with and
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 Pad\'e-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 .Comment: Revtex, 40 pages, 3 figures, and 8 pictograms (included in equations
Quantum phase transitions and thermodynamic properties in highly anisotropic magnets
The systems exhibiting quantum phase transitions (QPT) are investigated
within the Ising model in the transverse field and Heisenberg model with
easy-plane single-site anisotropy. Near QPT a correspondence between parameters
of these models and of quantum phi^4 model is established. A scaling analysis
is performed for the ground-state properties. The influence of the external
longitudinal magnetic field on the ground-state properties is investigated, and
the corresponding magnetic susceptibility is calculated. Finite-temperature
properties are considered with the use of the scaling analysis for the
effective classical model proposed by Sachdev. Analytical results for the
ordering temperature and temperature dependences of the magnetization and
energy gap are obtained in the case of a small ground-state moment. The forms
of dependences of observable quantities on the bare splitting (or magnetic
field) and renormalized splitting turn out to be different. A comparison with
numerical calculations and experimental data on systems demonstrating magnetic
and structural transitions (e.g., into singlet state) is performed.Comment: 46 pages, RevTeX, 6 figure
Five-loop additive renormalization in the phi^4 theory and amplitude functions of the minimally renormalized specific heat in three dimensions
We present an analytic five-loop calculation for the additive renormalization
constant A(u,epsilon) and the associated renormalization-group function B(u) of
the specific heat of the O(n) symmetric phi^4 theory within the minimal
subtraction scheme. We show that this calculation does not require new
five-loop integrations but can be performed on the basis of the previous
five-loop calculation of the four-point vertex function combined with an
appropriate identification of symmetry factors of vacuum diagrams. We also
determine the amplitude functions of the specific heat in three dimensions for
n=1,2,3 above T_c and for n=1 below T_c up to five-loop order. Accurate results
are obtained from Borel resummations of B(u) for n=1,2,3 and of the amplitude
functions for n=1. Previous conjectures regarding the smallness of the resummed
higher-order contributions are confirmed. Borel resummed universal amplitude
ratios A^+/A^- and a_c^+/a_c^- are calculated for n=1.Comment: 30 pages REVTeX, 3 PostScript figures, submitted to Phys. Rev.