2 research outputs found
Wilson-Polchinski exact renormalization group equation for O(N) systems: Leading and next-to-leading orders in the derivative expansion
With a view to study the convergence properties of the derivative expansion
of the exact renormalization group (RG) equation, I explicitly study the
leading and next-to-leading orders of this expansion applied to the
Wilson-Polchinski equation in the case of the -vector model with the
symmetry . As a test, the critical exponents and as well as the subcritical exponent (and higher ones) are estimated
in three dimensions for values of ranging from 1 to 20. I compare the
results with the corresponding estimates obtained in preceding studies or
treatments of other exact RG equations at second order. The
possibility of varying allows to size up the derivative expansion method.
The values obtained from the resummation of high orders of perturbative field
theory are used as standards to illustrate the eventual convergence in each
case. A peculiar attention is drawn on the preservation (or not) of the
reparametrisation invariance.Comment: Dedicated to Lothar Sch\"afer on the occasion of his 60th birthday.
Final versio
Critical equation of state of randomly dilute Ising systems
We determine the critical equation of state of three-dimensional randomly
dilute Ising systems, i.e. of the random-exchange Ising universality class. We
first consider the small-magnetization expansion of the Helmholtz free energy
in the high-temperature phase. Then, we apply a systematic approximation scheme
of the equation of state in the whole critical regime, that is based on
polynomial parametric representations matching the small-magnetization of the
Helmholtz free energy and satisfying a global stationarity condition. These
results allow us to estimate several universal amplitude ratios, such as the
ratio A^+/A^- of the specific-heat amplitudes. Our best estimate A^+/A^-=1.6(3)
is in good agreement with experimental results on dilute uniaxial
antiferromagnets.Comment: 21 pages, 1 figure, refs adde