Optimization of field-dependent nonperturbative renormalization group flows

We investigate the influence of the momentum cutoff function on the field-dependent nonperturbative renormalization group flows for the three-dimensional Ising model, up to the second order of the derivative expansion. We show that, even when dealing with the full functional dependence of the renormalization functions, the accuracy of the critical exponents can be simply optimized, through the principle of minimal sensitivity, which yields $\ensuremath{\nu}=0.628$ and $\ensuremath{\eta}=0.044$.

[1]  C. Bervillier.  The Wilson–Polchinski exact renormalization group equation , 2004, hep-th/0405025.

[2]  H. Chaté,et al.  Quantitative phase diagrams of branching and annihilating random walks. , 2004, Physical review letters.

[3]  L. Canet,et al.  Nonperturbative renormalization-group study of reaction-diffusion processes. , 2003, Physical review letters.

[4]  M. Tissier,et al.  Nonperturbative renormalization-group approach to frustrated magnets , 2003, cond-mat/0309101.

[5]  P. Le Doussal,et al.  Functional renormalization group and the field theory of disordered elastic systems. , 2003, Physical review. E, Statistical, nonlinear, and soft matter physics.

[6]  J. Vidal,et al.  Nonperturbative renormalization group approach to the Ising model: A derivative expansion at order ∂4 , 2003, hep-th/0302227.

[7]  P. Le Doussal,et al.  Higher correlations, universal distributions, and finite size scaling in the field theory of depinning. , 2003, Physical review. E, Statistical, nonlinear, and soft matter physics.

[8]  J. Vidal,et al.  Optimization of the derivative expansion in the nonperturbative renormalization group , 2002, hep-th/0211055.

[9]  C. Wetterich,et al.  Phase transition and critical behavior of the d=3 Gross-Neveu model , 2002, cond-mat/0203588.

[10]  D. Litim.  Critical exponents from optimised renormalisation group flows , 2002, hep-th/0203006.

[11]  D. Litim.  Derivative expansion and renormalisation group flows , 2001, hep-th/0111159.

[12]  M. Hasenbusch.  MONTE CARLO STUDIES OF THE THREE-DIMENSIONAL ISING MODEL IN EQUILIBRIUM , 2001 .

[13]  D. Zappalà,et al.  Proper time regulator and renormalization group flow , 2001, hep-th/0106230.

[14]  D. Litim.  Optimized renormalization group flows , 2001, hep-th/0103195.

[15]  C. Wetterich,et al.  Phase transitions in liquid 3He. , 2001, Physical review letters.

[16]  C. Wetterich,et al.  Phase transitions in liquid helium 3 , 2000, cond-mat/0008332.

[17]  C. Wetterich,et al.  Critical exponents of the Gross-Neveu model from the effective average action. , 2000, Physical review letters.

[18]  C. Wetterich,et al.  Non-perturbative renormalization flow in quantum field theory and statistical physics , 2000, hep-ph/0005122.

[19]  C. Bervillier,et al.  Exact renormalization group equations. An Introductory review , 2000, hep-th/0002034.

[20]  T. Morris,et al.  Convergence of derivative expansions of the renormalization group , 1999, hep-th/9906166.

[21]  M. Strickland,et al.  Optimization of renormalization group flow , 1999, hep-th/9905206.

[22]  M. Strickland,et al.  Application of Renormalization Group Techniques to a Homogeneous Bose Gas at Finite Temperature , 1998, cond-mat/9811096.

[23]  C. Wetterich,et al.  Equation of state near the endpoint of the critical line , 1998, cond-mat/9806372.

[24]  J. Zinn-Justin,et al.  Critical exponents of the N-vector model , 1998, cond-mat/9803240.

[25]  W. Souma,et al.  Rapidly Converging Truncation Scheme of the Exact Renormalization Group , 1998, hep-th/9803056.

[26]  A. Travesset,et al.  O(N) models within the local potential approximation , 1997, hep-th/9701028.

[27]  Thomas Papenbrock,et al.  Two-loop results from improved one loop computations , 1995 .

[28]  Freire,et al.  Phase diagram of superconductors from nonperturbative flow equations. , 1995, Physical review. B, Condensed matter.

[29]  J. Latorre,et al.  SCHEME INDEPENDENCE AND THE EXACT RENORMALIZATION GROUP , 1994, hep-th/9411122.

[30]  G. Zumbach,et al.  The renormalization group in the local potential approximation and its applications to the O ( n) model , 1994 .

[31]  T. Morris.  The Exact renormalization group and approximate solutions , 1993, hep-ph/9308265.

[32]  U. Ellwanger.  Flow equations forN point functions and bound states , 1993, hep-ph/9308260.

[33]  C. Wetterich,et al.  Critical Exponents from the Effective Average Action , 1993, hep-ph/9308214.

[34]  C. Wetterich,et al.  Exact evolution equation for the effective potential , 1993, 1710.05815.

[35]  Fisher,et al.  Interface fluctuations in disordered systems: 5- epsilon expansion and failure of dimensional reduction. , 1986, Physical review letters.

[36]  P. Stevenson.  Optimized Perturbation Theory , 1981 .

[37]  I. G. Halliday,et al.  Anharmonic oscillator: A new approach , 1980 .

[38]  A. Houghton,et al.  Renormalization group equation for critical phenomena , 1973 .

[39]  Bagnuls,et al.  Field-theoretical approach to critical phenomena. , 1990, Physical review. B, Condensed matter.