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Renormalization group approach to the P versus NP question [article]

S.N. Coppersmith
2006 arXiv   pre-print
The paper presents a renormalization group transformation that maps an arbitrary Boolean function of N Boolean variables to one of N-1 variables.  ...  This paper argues that the ideas underlying the renormalization group technique used to characterize phase transitions in condensed matter systems could be useful for distinguishing computational complexity  ...  Progress on this issue is the key to using the RG approach to be able to address the P versus NP question.  ... 
arXiv:cs/0608053v2 fatcat:tra235efvbf4bmp2opim7zvp2m

Renormalization group approach to satisfiability [article]

S.N. Coppersmith
2006 arXiv   pre-print
Here, a renormalization group transformation is constructed and used to relate the properties of satisfiability problems with different numbers of variables in each clause.  ...  The transformation yields new insight into phase transitions delineating "hard" and "easy" satisfiability problems.  ...  the renormalization group procedure can transform the problem out of NP and even PSPACE altogether.  ... 
arXiv:cond-mat/0509160v2 fatcat:5i24z7cgnrffnkqby3yt7j6ule

Using the Renormalization Group to Classify Boolean Functions

S. N. Coppersmith
2008 Journal of statistical physics  
This paper argues that the renormalization group technique used to characterize phase transitions in condensed matter systems can be used to classify Boolean functions.  ...  A renormalization group transformation is presented that maps an arbitrary Boolean function of N Boolean variables to one of N −1 variables.  ...  Progress on this issue is the key to using the RG approach to be able to address the P versus NP question.  ... 
doi:10.1007/s10955-008-9486-2 fatcat:7efwhxvearc57bwb6coagfausu

Page 3995 of Mathematical Reviews Vol. , Issue 98F [page]

1998 Mathematical Reviews  
The authors study the question of whether the renormalization group is well defined on the set of Gibbs measures.  ...  (DK-CPNH-B; Copenhagen); Sakai, Norisuke (J-TOK YTE-P; Meguro) Renormalization group approach to multiple-arc random matrix models. (English summary) Phys. Lett. B 398 (1997), no. 1-2, 123-129.  ... 

Critical Slowing Down in One-Dimensional Maps and Beyond

Bailin Hao
2005 Journal of statistical physics  
There is a cross-over to D 0 = 0.538 . . . when the order goes to infinity, i.e., to the Feigenbaum accumulation point.  ...  The problem of whether there exists a "super-scaling" for the dimension spectrum D W q that does not depend on the primitive word W underlying the period-n-tupling sequence seems to remain open.  ...  Pedagogically speaking, it provides a nice paradigm to elucidate the idea and technique of renormalization group approach in statistical physics without requiring the heavy machinery of quantum field theory  ... 
doi:10.1007/s10955-005-8669-3 fatcat:52vy724gp5f55j3lviqthodykq

Nonperturbative functional renormalization group for random field models and related disordered systems. II. Results for the random fieldO(N)model

Matthieu Tissier, Gilles Tarjus
2008 Physical Review B  
We study the critical behavior and phase diagram of the d-dimensional random field O(N) model by means of the nonperturbative functional renormalization group approach presented in the preceding paper.  ...  Below d_DR(N), our formalism gives access to both the typical behavior of the system, controlled by zero-temperature fixed points with a nonanalytic dimensionless effective action, and to the physics of  ...  CONCLUSION AND PERSPECTIVES In this paper, which is the second part of a series of articles reporting our work on a nonperturbative functional renormalization group (NP-FRG) approach for random field models  ... 
doi:10.1103/physrevb.78.024204 fatcat:gimnxhandzelrd6mouzql6ywre

Extending the QCD Perturbative Domain to Higher Energies [article]

Marcello Ciafaloni
2003 arXiv   pre-print
After a brief introduction to low-x QCD and to resummation approaches, I illustrate the predictions for the gluon Green function and splitting function of a recent renormalization-group improved small-x  ...  I argue, on this basis, that the range of validity of perturbative calculations is considerably extended in rapidity with respect to leading log expectations.  ...  I also thank Guido Altarelli and Stefano Forte for various conversations on similarities and differences of the duality approach.  ... 
arXiv:hep-ph/0310110v1 fatcat:dwpc3l6o3zcorcgkafmbdztwpq

Chiral Symmetry and the Nucleon-Nucleon Interaction [article]

R. Machleidt, D. R. Entem
2011 arXiv   pre-print
We summarize the current status of our understanding of nuclear forces based upon chiral symmetry--an idea that was advocated by Gerry Brown already several decades ago.  ...  Acknowledgement It is our great pleasure to dedicate this chapter to Gerry Brown on the occasion of his 85th birthday. References [1] G. E. Brown, Comments Nucl. Part. Phys. 4 (1970) 140.  ...  To answer this question, we show in Table 1 the χ 2 /datum for the fit of the world np data below 290 MeV for families of np potentials at NLO and NNLO constructed by the Juelich group [89] .  ... 
arXiv:1110.3022v1 fatcat:tj7g32uuujbsbkiodlfjnbityi

Page 1828 of Mathematical Reviews Vol. , Issue 2003C [page]

2003 Mathematical Reviews  
The renormalization-group construction allows us to obtain the dispersion relation of these modes, i.e. their damping rate versus the wavenumber.  ...  Moreover, a renormalization-group method is presented in order to construct the hydrodynamic and reactive modes of relaxation in chaotic models.  ... 

Dimensional reduction breakdown and correction to scaling in the random-field Ising model [article]

Ivan Balog, Gilles Tarjus, Matthieu Tissier
2020 arXiv   pre-print
We provide a theoretical analysis by means of the nonperturbative functional renormalization group (NP-FRG) of the corrections to scaling in the critical behavior of the random-field Ising model (RFIM)  ...  We show that the NP-FRG results are in very good agreement with recent large-scale lattice simulations of the RFIM in d=5 and we detail the consequences for the leading correction-to-scaling exponent of  ...  Acknowledgments IB acknowledges the support of the Croatian Science Foundation Project No.  ... 
arXiv:2008.13650v1 fatcat:m3i2xe7gbvdm7lmvibcyr5iyyy

Higgs mass bounds from renormalization flow for a simple Yukawa model

Holger Gies, Clemens Gneiting, René Sondenheimer
2014 Physical Review D  
We study the functional renormalization group flow of a Higgs-Yukawa toy model mimicking the top-Higgs sector of the standard model. This approach allows for treating arbitrary bare couplings.  ...  By contrast, more general bare potentials allow to diminish the lower bound considerably. We identify a simple renormalization group mechanism for this depletion of the lower bound.  ...  HG and RS acknowledge support by the DFG under grants GRK1523, Gi 328/5-2 (Heisenberg program).  ... 
doi:10.1103/physrevd.89.045012 fatcat:fohsfzrd7favlp6e53oporeapu

One-loop electroweak corrections for polarized Moller scattering at different renormalization schemes and conditions [article]

A. Aleksejevs, S. Barkanova, A. Ilyichev, Y. Kolomensky, V. Zykunov
2011 arXiv   pre-print
Using two different approaches, we perform updated and detailed calculations of the complete one-loop (Next-to-Leading Order (NLO)) set of electroweak radiative corrections to the parity violating e- e  ...  The numerical results obtained within the on-shell renormalization scheme using two different sets of renormalization conditions are in excellent agreement.  ...  As is well known, only the sum of both groups is gauge invariant; later we show that both approaches give exactly the same results for the observable asymmetry.  ... 
arXiv:1010.4185v3 fatcat:pjsmpba6ybfhbisglnoqdfndwq

On the Renormalization of the One–Pion Exchange Potential and the Consistency of Weinberg's Power Counting

E. Epelbaum, Ulf-G. Meißner
2012 Few-body systems  
In this paper we discuss the role the cutoff plays in the application of chiral effective field theory to the two-nucleon system and study carefully the cutoff-dependence of phase shifts and observables  ...  We show that (i) there is no need to use the momentum-space cutoff larger than Lambda 3 fm^(-1); (ii) the neutron-proton low-energy data show no evidence for an inconsistency of Weinberg's power counting  ...  One of the authors (E.E.) wishes to thank the organizers of the workshop "Nuclear Forces and QCD: Never the Twain Shall Meet", held at ECT* in Trento June, 20 to July, 1, 2005, where part of this work  ... 
doi:10.1007/s00601-012-0492-1 fatcat:uibjreiydra7vlddkshzqtjk6u

Nonperturbative Condensates in the Electroweak Phase-Transition [article]

Bastian Bergerhoff, Christof Wetterich
1995 arXiv   pre-print
Wetterich at the 3rd Colloque Cosmologie, Paris, June 7-9, 1995, to appear in the proceedings)  ...  This is due to the dominance of three-dimensional physics at high temperatures which implies that the effective gauge coupling grows strong in the symmetric phase.  ...  In all plots we use four dimensional quantities and plot δU = U 4 (Φ) − U 4 (0) versus (1) ) corresponds to the critical temperature which would be obtained from our renormalization groupimproved approach  ... 
arXiv:hep-ph/9508352v2 fatcat:hqdj3iox2zfvtgzxyye6lfylyq

QCD Running Coupling: Freezing Versus Enhancement in the Infrared Region [article]

Aleksey I. Alekseev
1998 arXiv   pre-print
It is shown that the requirements of asymptotic freedom, analyticity, confinement and the value of the gluon condensate are compatible in the framework of our approach.  ...  Possibilities to find an agreement of the enhanced behaviour of the running coupling constant with integral estimations in the infrared region are also discussed.  ...  Let us represent expression (7) in explicitly renormalization invariant form. It can be done without solving the differential renormalization group equations.  ... 
arXiv:hep-ph/9802372v1 fatcat:hwhzttmqafag3p7bo7p4o6c7y4
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