Nonperturbative renormalization group approach to the Ising model: A derivative expansion at order ∂4

On the example of the three-dimensional Ising model, we show that nonperturbative renormalization group equations allow one to obtain very accurate critical exponents. Implementing the order ∂ 4 of the derivative expansion leads to v=0.632 and to an anomalous dimension η=0.033 which is significantly improved compared with lower orders calculations.

[1]  Ulrich Ellwanger.  Flow equations forN point functions and bound states , 1994 .

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

[3]  C. Bervillier,et al.  Exact renormalization group equations. An Introductory review , 2000 .

[4]  Proper time regulator and renormalization group flow , 2001, hep-th/0106230.

[5]  C. Wetterich,et al.  Non-perturbative renormalization flow in quantum field theory and statistical physics , 2002 .

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

[7]  Polchinski equation, reparameterization invariance and the derivative expansion , 1997, hep-th/9705129.

[8]  C. Wetterich,et al.  Two loop results from one loop computations and non perturbative solutions of exact evolution equations , 1994 .

[9]  Tim R. Morris.  The Exact renormalization group and approximate solutions , 1994 .

[10]  I. Herbut,et al.  renormalization group , 1999 .

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

[12]  J. Vidal,et al.  Optimization of the derivative expansion in the nonperturbative renormalization group , 2003 .

[13]  J. Vidal,et al.  Randomly dilute Ising model: A nonperturbative approach , 2001, cond-mat/0109176.

[14]  Daniel F. Litim.  Critical exponents from optimised renormalisation group flows , 2002 .

[15]  M. Tissier,et al.  XY frustrated systems: Continuous exponents in discontinuous phase transitions , 2001, cond-mat/0107183.

[16]  SCHEME INDEPENDENCE AND THE EXACT RENORMALIZATION GROUP , 1994, hep-th/9411122.

[17]  Delamotte,et al.  Frustrated heisenberg magnets: A nonperturbative approach , 2000, Physical review letters.

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

[19]  Critical exponents of the N-vector model , 1998, cond-mat/9803240.

[20]  C. Wetterich,et al.  Phase transition and critical behavior of the d=3 Gross-Neveu model , 2002 .

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

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