Geodesic
$p$-Adic Pseudodifferential Operators and Analytic Continuation of Replica Matrices
Teoretičeskaâ i matematičeskaâ fizika, Tome 144 (2005) no. 2, pp. 336-341 Cet article a éte moissonné depuis la source Math-Net.Ru

Voir la notice de l'article

We consider the procedure for analytic continuation of the replica matrix. We formulate a particular form of this procedure in which the analytic continuation is defined by a sequence of maps. Using this definition, we construct a solution that breaks the Parisi replica symmetry and find the corresponding $p$-adic pseudodifferential operator.
Keywords: $p$-adic pseudodifferential operators, replica method. 
@article{TMF_2005_144_2_a10,
     author = {A. Yu. Khrennikov and S. V. Kozyrev},
     title = {$p${-Adic} {Pseudodifferential} {Operators} and {Analytic} {Continuation} of {Replica} {Matrices}},
     journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
     pages = {336--341},
     year = {2005},
     volume = {144},
     number = {2},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TMF_2005_144_2_a10/}
}
TY  - JOUR
AU  - A. Yu. Khrennikov
AU  - S. V. Kozyrev
TI  - $p$-Adic Pseudodifferential Operators and Analytic Continuation of Replica Matrices
JO  - Teoretičeskaâ i matematičeskaâ fizika
PY  - 2005
SP  - 336
EP  - 341
VL  - 144
IS  - 2
UR  - http://geodesic.mathdoc.fr/item/TMF_2005_144_2_a10/
LA  - ru
ID  - TMF_2005_144_2_a10
ER  - 
%0 Journal Article
%A A. Yu. Khrennikov
%A S. V. Kozyrev
%T $p$-Adic Pseudodifferential Operators and Analytic Continuation of Replica Matrices
%J Teoretičeskaâ i matematičeskaâ fizika
%D 2005
%P 336-341
%V 144
%N 2
%U http://geodesic.mathdoc.fr/item/TMF_2005_144_2_a10/
%G ru
%F TMF_2005_144_2_a10
A. Yu. Khrennikov; S. V. Kozyrev. $p$-Adic Pseudodifferential Operators and Analytic Continuation of Replica Matrices. Teoretičeskaâ i matematičeskaâ fizika, Tome 144 (2005) no. 2, pp. 336-341. http://geodesic.mathdoc.fr/item/TMF_2005_144_2_a10/

[1] M. Mezard, G. Parisi, M. Virasoro, Spin-Glass Theory and Beyond, World Scientific, Singapore, 1987 | MR | Zbl

[2] V. A. Avetisov, A. H. Bikulov, S. V. Kozyrev, J. Phys. A, 32 (1999), 8785–8791 ; ; G. Parisi, N. Sourlas, Eur. J. Phys. B, 14 (2000), 535–542 ; E-print cond-mat/9904360E-print cond-mat/9906095 | DOI | MR | Zbl | DOI | MR

[3] S. V. Kozyrev, Izv. RAN. Ser. matem., 66:2 (2002), 149–158 ; ; ТМФ, 138:3 (2004), 322–332 ; ; В. С. Владимиров, И. В. Волович, Е. И. Зеленов, $p$-Адический анализ и математическая физика, Наука, М., 1994 ; I. V. Volovich, Class. Q Grav., 4 (1987), L83–L87 ; A. Khrennikov, $p$-Adic Valued Distributions in Mathematical Physics, Kluwer Acad. Publ., Dordrecht, 1994 ; Non–Archimedean Analysis: Quantum Paradoxes, Dynamical Systems and Biological Models, Kluwer, Dordrecht, 1997 ; V. A. Avetisov, A. H. Bikulov, S. V. Kozyrev, V. A. Osipov, J. Phys. A, 35 (2002), 177–189 ; E-print math-ph/0012019E-print math-ph/0303045E-print cond-mat/0106506 | DOI | MR | Zbl | DOI | MR | Zbl | MR | Zbl | DOI | MR | MR | MR | Zbl | DOI | MR | Zbl

[4] A. Yu. Khrennikov, S. V. Kozyrev, Pseudodifferential operators on ultrametric spaces and ultrametric wavelets, Preprint of MSI No 02143, MSI; Växjö Univ., Växjö, Sweden, 2002 | MR