Colli, Pierluigi; Gilardi, Gianni; Sprekels, Jürgen Optimal control of a phase field system of Caginalp type with fractional operators. (English) Zbl 1505.35242 Pure Appl. Funct. Anal. 7, No. 5, 1597-1635 (2022). MSC: 35K45 35K90 35R11 46B15 49J20 49K20 PDFBibTeX XMLCite \textit{P. Colli} et al., Pure Appl. Funct. Anal. 7, No. 5, 1597--1635 (2022; Zbl 1505.35242) Full Text: arXiv Link
Mukhamedov, Farrukh; El Gheteb, Soueidy Quantum Ising model with generalized competing XY-interactions on a Cayley tree. (English) Zbl 1510.46037 Infin. Dimens. Anal. Quantum Probab. Relat. Top. 25, No. 3, Article ID 2250010, 33 p. (2022). MSC: 46L53 60J99 46L60 60G50 82B10 81Q10 PDFBibTeX XMLCite \textit{F. Mukhamedov} and \textit{S. El Gheteb}, Infin. Dimens. Anal. Quantum Probab. Relat. Top. 25, No. 3, Article ID 2250010, 33 p. (2022; Zbl 1510.46037) Full Text: DOI
Mukhamedov, Farrukh; Khakimov, Otabek Translation-invariant generalized \(p\)-adic Gibbs measures for the Ising model on Cayley trees. (English) Zbl 1477.82009 Math. Methods Appl. Sci. 44, No. 16, 12302-12316 (2021). Reviewer: Hasan Akin (Trieste) MSC: 82B26 82B20 46S10 39A70 47H10 60K35 PDFBibTeX XMLCite \textit{F. Mukhamedov} and \textit{O. Khakimov}, Math. Methods Appl. Sci. 44, No. 16, 12302--12316 (2021; Zbl 1477.82009) Full Text: DOI
Laca, Marcelo; Warren, Jacqueline M. Phase transitions on \(C^*\)-algebras arising from number fields and the generalized Furstenberg conjecture. (English) Zbl 1449.46057 J. Oper. Theory 83, No. 1, 73-93 (2020). Reviewer: Thomas B. Ward (Leeds) MSC: 46L55 11M55 58B34 37A44 46L30 PDFBibTeX XMLCite \textit{M. Laca} and \textit{J. M. Warren}, J. Oper. Theory 83, No. 1, 73--93 (2020; Zbl 1449.46057) Full Text: arXiv
Takeishi, Takuya Bost-Connes systems for local fields of characteristic zero. (English) Zbl 1410.82003 Int. Math. Res. Not. 2018, No. 7, 2052-2069 (2018). MSC: 82B10 46L60 82B26 PDFBibTeX XMLCite \textit{T. Takeishi}, Int. Math. Res. Not. 2018, No. 7, 2052--2069 (2018; Zbl 1410.82003) Full Text: DOI arXiv
Burr, Michael; Gao, Shuhong; Knoll, Fiona Optimal bounds for Johnson-Lindenstrauss transformations. (English) Zbl 1480.46016 J. Mach. Learn. Res. 19, Paper No. 73, 22 p. (2018). MSC: 46B07 68Q17 PDFBibTeX XMLCite \textit{M. Burr} et al., J. Mach. Learn. Res. 19, Paper No. 73, 22 p. (2018; Zbl 1480.46016) Full Text: arXiv Link
Thomsen, Klaus Phase transition in \(O_{2}\). (English) Zbl 1370.46046 Commun. Math. Phys. 349, No. 2, 481-492 (2017). MSC: 46L55 46L30 PDFBibTeX XMLCite \textit{K. Thomsen}, Commun. Math. Phys. 349, No. 2, 481--492 (2017; Zbl 1370.46046) Full Text: DOI arXiv
Borisov, Denis I.; Znojil, Miloslav Mathematical and physical meaning of the crossings of energy levels in \(\mathcal {PT}\)-symmetric systems. (English) Zbl 1402.81149 Bagarello, Fabio (ed.) et al., Non-Hermitian Hamiltonians in quantum physics. Selected contributions from the 15th international conference on non-Hermitian Hamiltonians in quantum physics, Palermo, Italy, May 18–23, 2015. Cham: Springer (ISBN 978-3-319-31354-2/hbk; 978-3-319-31356-6/ebook). Springer Proceedings in Physics 184, 201-217 (2016). MSC: 81Q10 81Q12 46C05 PDFBibTeX XMLCite \textit{D. I. Borisov} and \textit{M. Znojil}, Springer Proc. Phys. 184, 201--217 (2016; Zbl 1402.81149) Full Text: DOI arXiv
Mukhamedov, Farrukh; Dogan, Mutlay On \(P\)-adic \(\lambda\)-model on the Cayley tree. II: Phase transitions. (English) Zbl 1321.82020 Rep. Math. Phys. 75, No. 1, 25-46 (2015). Reviewer: Guy Jumarie (Montréal) MSC: 82B26 46S10 12J12 39A70 47H10 60K35 PDFBibTeX XMLCite \textit{F. Mukhamedov} and \textit{M. Dogan}, Rep. Math. Phys. 75, No. 1, 25--46 (2015; Zbl 1321.82020) Full Text: DOI
Accardi, Luigi; Mukhamedov, Farrukh; Saburov, Mansoor On quantum Markov chains on Cayley tree. III: Ising model. (English) Zbl 1316.46046 J. Stat. Phys. 157, No. 2, 303-329 (2014). MSC: 46L53 60J99 46L60 60G50 82B20 82B26 82B27 PDFBibTeX XMLCite \textit{L. Accardi} et al., J. Stat. Phys. 157, No. 2, 303--329 (2014; Zbl 1316.46046) Full Text: DOI arXiv
Mukhamedov, Farrukh On dynamical systems and phase transitions for \(q + 1\)-state \(p\)-adic Potts model on the Cayley tree. (English) Zbl 1280.46047 Math. Phys. Anal. Geom. 16, No. 1, 49-87 (2013). Reviewer: Hasan Akin (Gaziantep) MSC: 46S10 82B26 82B20 37N20 PDFBibTeX XMLCite \textit{F. Mukhamedov}, Math. Phys. Anal. Geom. 16, No. 1, 49--87 (2013; Zbl 1280.46047) Full Text: DOI arXiv
Crisp, Tyrone The Bost-Connes phase transition and unitary representations. (English) Zbl 1275.46052 J. Noncommut. Geom. 7, No. 1, 291-300 (2013). Reviewer: Nadia Larsen (Oslo) MSC: 46L55 22D10 PDFBibTeX XMLCite \textit{T. Crisp}, J. Noncommut. Geom. 7, No. 1, 291--300 (2013; Zbl 1275.46052) Full Text: DOI
Accardi, Luigi; Mukhamedov, Farrukh; Saburov, Mansoor On quantum Markov chains on Cayley tree. II: Phase transitions for the associated chain with \(XY\)-model on the Cayley tree of order three. (English) Zbl 1237.82009 Ann. Henri Poincaré 12, No. 6, 1109-1144 (2011). Reviewer: Adam Skalski (Warszawa) MSC: 82B26 82B10 46L53 60J99 PDFBibTeX XMLCite \textit{L. Accardi} et al., Ann. Henri Poincaré 12, No. 6, 1109--1144 (2011; Zbl 1237.82009) Full Text: DOI arXiv
Benaych-Georges, Florent; Nadakuditi, Raj Rao The eigenvalues and eigenvectors of finite, low rank perturbations of large random matrices. (English) Zbl 1226.15023 Adv. Math. 227, No. 1, 494-521 (2011). Reviewer: Martín Argerami (Regina) MSC: 15B52 15A18 46L54 60B20 62H25 82B26 PDFBibTeX XMLCite \textit{F. Benaych-Georges} and \textit{R. R. Nadakuditi}, Adv. Math. 227, No. 1, 494--521 (2011; Zbl 1226.15023) Full Text: DOI arXiv
Laca, Marcelo; Raeburn, Iain Phase transition on the Toeplitz algebra of the affine semigroup over the natural numbers. (English) Zbl 1203.46045 Adv. Math. 225, No. 2, 643-688 (2010). MSC: 46L55 47L80 PDFBibTeX XMLCite \textit{M. Laca} and \textit{I. Raeburn}, Adv. Math. 225, No. 2, 643--688 (2010; Zbl 1203.46045) Full Text: DOI arXiv
Laca, Marcelo; Larsen, Nadia S.; Neshveyev, Sergey Hecke algebras of semidirect products and the finite part of the Connes-Marcolli \(C^*\)-algebra. (English) Zbl 1136.46045 Adv. Math. 217, No. 2, 449-488 (2008). MSC: 46L55 20C08 20G35 58B34 82B10 PDFBibTeX XMLCite \textit{M. Laca} et al., Adv. Math. 217, No. 2, 449--488 (2008; Zbl 1136.46045) Full Text: DOI arXiv
Mil’man, V. D. Phenomena that occur in high dimensions. (English. Russian original) Zbl 1079.46005 Russ. Math. Surv. 59, No. 1, 159-169 (2004); translation from Usp. Mat. Nauk 59, No. 1, 157-168 (2004). Reviewer: A. E. Litvak (Edmonton) MSC: 46B07 52A21 46B09 52A20 46-02 52-02 PDFBibTeX XMLCite \textit{V. D. Mil'man}, Russ. Math. Surv. 59, No. 1, 159--169 (2003; Zbl 1079.46005); translation from Usp. Mat. Nauk 59, No. 1, 157--168 (2004) Full Text: DOI
Litvak, A. E.; Milman, V. D. Euclidean sections of direct sums of normed spaces. (English) Zbl 1074.46005 Can. Math. Bull. 46, No. 2, 242-251 (2003). Reviewer: Mikhail Ostrovskii (Queens) MSC: 46B07 46B09 52A21 PDFBibTeX XMLCite \textit{A. E. Litvak} and \textit{V. D. Milman}, Can. Math. Bull. 46, No. 2, 242--251 (2003; Zbl 1074.46005) Full Text: DOI
Mankiewicz, P.; Tomczak-Jaegermann, N. Geometry of families of random projections of symmetric convex bodies. (English) Zbl 1033.46011 Geom. Funct. Anal. 11, No. 6, 1282-1326 (2001). Reviewer: Daniel Hug (Freiburg) MSC: 46B07 52A21 46B09 46B20 PDFBibTeX XMLCite \textit{P. Mankiewicz} and \textit{N. Tomczak-Jaegermann}, Geom. Funct. Anal. 11, No. 6, 1282--1326 (2001; Zbl 1033.46011) Full Text: DOI
Gukov, Sergei; Periwal, Vipul \(D\)-brane phase transitions and monodromy in \(K\)-theory. (English) Zbl 0970.81067 J. Geom. Phys. 34, No. 3-4, 263-269 (2000). MSC: 81T30 81T40 14J28 46L80 PDFBibTeX XMLCite \textit{S. Gukov} and \textit{V. Periwal}, J. Geom. Phys. 34, No. 3--4, 263--269 (2000; Zbl 0970.81067) Full Text: DOI arXiv
Garet, Olivier Gibbsian fields associated to exponentially decreasing quadratic potentials. (English) Zbl 0923.46072 Ann. Inst. Henri Poincaré, Probab. Stat. 35, No. 3, 387-415 (1999). Reviewer: Chandra Shekhar Sharma (London) MSC: 46N30 46N55 60G15 82B23 82B26 PDFBibTeX XMLCite \textit{O. Garet}, Ann. Inst. Henri Poincaré, Probab. Stat. 35, No. 3, 387--415 (1999; Zbl 0923.46072) Full Text: DOI Numdam EuDML
Ganikhodjaev, N. N.; Mukhamedov, F. M.; Rozikov, U. A. On nonarchimedean Ising models. (Russian) Zbl 0980.46055 Dokl. Akad. Nauk Resp. Uzb., Mat. Tekh. Nauki Estestvozn. 1998, No. 11, 6-9 (1998). MSC: 46S10 81T10 81V45 47S10 PDFBibTeX XMLCite \textit{N. N. Ganikhodjaev} et al., Dokl. Akad. Nauk Resp. Uzb., Mat. Tekh. Nauki Estestvozn. 1998, No. 11, 6--9 (1998; Zbl 0980.46055)
Danilov, V. G.; Omel’yanov, G. A. Propagation of singularities and related problems of solidification. (English) Zbl 0947.46032 Mat. Vesn. 49, No. 2, 143-150 (1997). Reviewer: Zoran Kadelburg (Zemun) MSC: 46F99 35B32 35D99 47J15 PDFBibTeX XMLCite \textit{V. G. Danilov} and \textit{G. A. Omel'yanov}, Mat. Vesn. 49, No. 2, 143--150 (1997; Zbl 0947.46032)
Fröman, Nanny; Fröman, Per Olof Phase-integral method: allowing nearlying transition points. With adjoined papers by A. Dzieciol, the authors, A. Hökback, S. Linnaeus, B. Lundborg and E. Walles. (English) Zbl 0887.46047 Springer Tracts in Natural Philosophy. 40. Berlin: Springer-Verlag. x, 250 p. DM 138.00; öS 1007.40; sFr. 132.50 (1996). Reviewer: Valentin Zagrebnov (Marseille) MSC: 46N50 81Q20 47N50 46-02 81-02 PDFBibTeX XMLCite \textit{N. Fröman} and \textit{P. O. Fröman}, Phase-integral method: allowing nearlying transition points. With adjoined papers by A. Dzieciol, the authors, A. Hökback, S. Linnaeus, B. Lundborg and E. Walles. Berlin: Springer-Verlag (1996; Zbl 0887.46047)
Bost, J.-B.; Connes, A. Hecke algebras, type III factors and phase transitions with spontaneous symmetry breaking in number theory. (English) Zbl 0842.46040 Sel. Math., New Ser. 1, No. 3, 411-457 (1995). MSC: 46L55 11M55 46L35 11M06 11R18 20G30 82B10 82B26 PDFBibTeX XMLCite \textit{J. B. Bost} and \textit{A. Connes}, Sel. Math., New Ser. 1, No. 3, 411--457 (1995; Zbl 0842.46040) Full Text: DOI
Dineykhan, M.; Efimov, G. V.; Ganbold, G.; Nedelko, S. N. Oscillator representation in quantum physics. (English) Zbl 0834.47065 Lecture Notes in Physics. New Series m: Monographs. 26. Berlin: Springer- Verlag. ix, 279 p. (1995). Reviewer: G.Loupias (Montpellier) MSC: 47N50 81-02 81Q05 81S40 81T40 46G12 22E70 PDFBibTeX XMLCite \textit{M. Dineykhan} et al., Oscillator representation in quantum physics. Berlin: Springer-Verlag (1995; Zbl 0834.47065) Full Text: DOI
Pustyl’nikov, L. D. On a ground state in the Frenkel-Kontorova model and metric properties of mappings of standard type. (English) Zbl 0816.60095 Dobrushin, R. L. (ed.), Probability contributions to statistical mechanics. Transl. by A. S. Sossinsky. Providence, RI: American Mathematical Society. Adv. Sov. Math. 20, 277-289 (1994). Reviewer: S.Pogosian (Erevan) MSC: 60K35 82B20 46N10 37A99 PDFBibTeX XMLCite \textit{L. D. Pustyl'nikov}, Adv. Sov. Math. 20, 277--289 (1994; Zbl 0816.60095)
Bost, Jean Benoît; Connes, Alain Euler products and type III factors. (Produits eulériens et facteurs de type III.) (French. English summary) Zbl 0781.46045 C. R. Acad. Sci., Paris, Sér. I 315, No. 3, 279-284 (1992). Reviewer: P.E.T.Jorgensen (Iowa City) MSC: 46L10 46L35 11M06 PDFBibTeX XMLCite \textit{J. B. Bost} and \textit{A. Connes}, C. R. Acad. Sci., Paris, Sér. I 315, No. 3, 279--284 (1992; Zbl 0781.46045)
Alberti, Peter M. A study on the geometry of pairs of positive linear forms, algebraic transition probability and geometrical phase over non-commutative operator algebras. I. (English) Zbl 0792.46037 Z. Anal. Anwend. 11, No. 3, 293-334 (1992). Reviewer: G.A.Elliott (Toronto) MSC: 46L05 46L10 46L51 46L53 46L54 PDFBibTeX XMLCite \textit{P. M. Alberti}, Z. Anal. Anwend. 11, No. 3, 293--334 (1992; Zbl 0792.46037) Full Text: DOI
Alberti, Peter M. A study on the geometry of pairs of positive linear forms, algebraic transition probability and geometrical phase over non-commutative operator algebras. II. (English) Zbl 0792.46038 Z. Anal. Anwend. 11, No. 4, 455-488 (1992). Reviewer: G.A.Elliott (Toronto) MSC: 46L05 46L10 46L51 46L53 46L54 PDFBibTeX XMLCite \textit{P. M. Alberti}, Z. Anal. Anwend. 11, No. 4, 455--488 (1992; Zbl 0792.46038) Full Text: DOI
Verbeure, A.; Zagrebnov, V. A. Phase transitions and algebra of fluctuation operators in an exactly soluble model of a quantum anharmonic crystal. (English) Zbl 0888.46054 J. Stat. Phys. 69, No. 1-2, 329-359 (1992). MSC: 46N55 82B26 82D25 PDFBibTeX XMLCite \textit{A. Verbeure} and \textit{V. A. Zagrebnov}, J. Stat. Phys. 69, No. 1--2, 329--359 (1992; Zbl 0888.46054) Full Text: DOI
Evans, David E. An algebraic approach to critical phenomena in two-dimensional lattice models. (English) Zbl 0705.46036 Mathematical methods in statistical mechanics, Proc. Conf., Leuven/Belg. 1988, Leuven Notes Math. Theor. Phys. 1, Series A: Mathematical Physics, 15-30 (1989). Reviewer: Y.P.Virchenko MSC: 46L60 82B20 46N50 PDFBibTeX XML
Carey, Alan L.; Evans, David E. The operator algebras of the two-dimensional Ising model. (English) Zbl 0691.46052 Braids, AMS-IMS-SIAM Jt. Summer Res. Conf., Santa Cruz/Calif. 1986, Contemp. Math. 78, 117-165 (1988). Reviewer: A.Wehrl MSC: 46N99 46L60 81P05 82B10 PDFBibTeX XML
Amann, Anton Chirality as a classical observable in algebraic quantum mechanics. (English) Zbl 0666.46058 Fractals, quasicrystals, chaos, knots and algebraic quantum mechanics, Proc. NATO Adv. Res. Workshop New Theor. Conc. Phys. Chem., Acquadredda di Maratea/Italy, NATO ASI Ser., Ser: C 235, 305-325 (1988). Reviewer: W.Slowikowski MSC: 46N99 81V55 81Q99 PDFBibTeX XML
Sakai, Shôichirô Perturbations and KMS states in C *-dynamical systems (generalization of the absence theorem of phase transition to continuous quantum systems). (English) Zbl 0638.46048 Operator algebras and mathematical physics, Proc. Summer. Conf., Iowa City/Iowa 1985, Contemp. Math. 62, 187-217 (1987). Reviewer: D.Petz MSC: 46L60 46L40 46L55 82B10 PDFBibTeX XML
Evans, David E. The \(C^ *\)-algebras of the two-dimensional Ising model. (English) Zbl 0612.46065 Quantum probability and applications II, Proc. 2nd Workshop, Heidelberg/Ger. 1984, Lect. Notes Math. 1136, 162-176 (1985). Reviewer: Chu Cho-ho MSC: 46L60 46N99 46L30 PDFBibTeX XML
Araki, Huzihiro; Matsui, Taku \(C^*\)-algebra approach to ground states of the XY-model. (English) Zbl 0565.46036 Statistical physics and dynamical systems. Rigorous results, Pap. 2nd Colloq. Workshop, Köszeg/Hung. 1984, Prog. Phys. 10, 17-39 (1985). MSC: 46L60 82B10 46N99 82B26 PDFBibTeX XML
Araki, Huzihiro; Evans, David E. On a \(C^*\)-algebra approach to phase transition in the two-dimensional Ising model. (English) Zbl 0535.46046 Commun. Math. Phys. 91, 489-503 (1983). MSC: 46L60 46N99 82B10 PDFBibTeX XMLCite \textit{H. Araki} and \textit{D. E. Evans}, Commun. Math. Phys. 91, 489--503 (1983; Zbl 0535.46046) Full Text: DOI
Sakai, Shoichiro Phase transition free states on UHF algebras. (English) Zbl 0513.46039 J. Funct. Anal. 46, 119-125 (1982). MSC: 46L30 46L55 46L35 PDFBibTeX XMLCite \textit{S. Sakai}, J. Funct. Anal. 46, 119--125 (1982; Zbl 0513.46039) Full Text: DOI
Alberti, Peter M. Wachsende Übergangswahrscheinlichkeiten und vollständig positive stochastische Transformationen. (German) Zbl 0511.46065 Wiss. Z., Karl-Marx-Univ. Leipz., Math.-Naturwiss. Reihe 31, 3-10 (1982). MSC: 46L60 82B26 PDFBibTeX XMLCite \textit{P. M. Alberti}, Wiss. Z., Karl-Marx-Univ. Leipz., Math.-Naturwiss. Reihe 31, 3--10 (1982; Zbl 0511.46065)
Balaban, T.; Gawedzki, K. A low temperature expansion for the pseudoscalar Yukawa model of quantum fields in two space-time dimensions. (English) Zbl 0509.46059 Ann. Inst. Henri Poincaré, Nouv. Sér., Sect. A 36, 271-400 (1982). MSC: 46N99 46F05 81T08 PDFBibTeX XMLCite \textit{T. Balaban} and \textit{K. Gawedzki}, Ann. Inst. Henri Poincaré, Nouv. Sér., Sect. A 36, 271--400 (1982; Zbl 0509.46059) Full Text: Numdam EuDML
Ohya, Masanori Dynamical process in linear response theory. (English) Zbl 0438.46049 Rep. Math. Phys. 16, 305-315 (1979). MSC: 46L55 46L60 82B26 PDFBibTeX XMLCite \textit{M. Ohya}, Rep. Math. Phys. 16, 305--315 (1979; Zbl 0438.46049) Full Text: DOI
Trych-Pohlmeyer, Ewa B. The stability properties of equilibrium states. (English) Zbl 0425.46053 Algebres d’operateurs et leurs applications en physique mathematique, Colloq. int. CNRS No. 274, Marseille 1977, 437-440 (1979). MSC: 46L60 82B26 46L55 46N99 PDFBibTeX XML
Dell’Antonio, G. (ed.); Doplicher, S. (ed.); Jona-Lasinio, G. (ed.) Mathematical problems in theoretical physics. International conference held in Rome, June 6–15, 1977. (English) Zbl 0416.46054 Lecture Notes in Physics. 80. Berlin-Heidelberg-New York: Springer- Verlag. VI, 438 p. DM 35.50; $ 17.80 (1978). Reviewer: A. G. Ramm MSC: 46N99 81-02 82-02 81T05 46-06 46-02 46L60 PDFBibTeX XML
Dynkin, E. B. Sufficient statistics and extreme points. (English) Zbl 0403.62009 Ann. Probab. 6, 705-730 (1978). MSC: 62B05 46A55 60J35 60J50 60K35 82B26 PDFBibTeX XMLCite \textit{E. B. Dynkin}, Ann. Probab. 6, 705--730 (1978; Zbl 0403.62009) Full Text: DOI
Sakai, Shoichiro Recent developments in the theory of unbounded derivations in \(C^*\)- algebras. (English) Zbl 0392.46040 \(C^*\)-Algebras Appl. Phys., Proc. 2nd Japan-USA Semin., Los Angeles 1977, Lect. Notes Math. 650, 85-122 (1978). MSC: 46L05 46L55 46L40 46L60 PDFBibTeX XML