Abstract:
A study is made of a new class of interactions for which there is uniqueness of a Gibbs
state in a whole space together with nonunlqueness of the state in a half-space. The method of reflection positivity is used to study these interactions.
Citation:
S. B. Shlosman, “Uniqueness and half-space nonuniqueness of gibbs states in Czech models”, TMF, 66:3 (1986), 430–444; Theoret. and Math. Phys., 66:3 (1986), 284–293
\Bibitem{Shl86}
\by S.~B.~Shlosman
\paper Uniqueness and half-space nonuniqueness of gibbs states in Czech models
\jour TMF
\yr 1986
\vol 66
\issue 3
\pages 430--444
\mathnet{http://mi.mathnet.ru/tmf4639}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=847435}
\transl
\jour Theoret. and Math. Phys.
\yr 1986
\vol 66
\issue 3
\pages 284--293
\crossref{https://doi.org/10.1007/BF01018227}
\isi{https://gateway.webofknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=Publons&SrcAuth=Publons_CEL&DestLinkType=FullRecord&DestApp=WOS_CPL&KeyUT=A1986E586400010}
Linking options:
https://www.mathnet.ru/eng/tmf4639
https://www.mathnet.ru/eng/tmf/v66/i3/p430
This publication is cited in the following 19 articles:
Abraham D. Newman Ch.M. Shlosman S., “A Continuum of Pure States in the Ising Model on a Halfplane”, J. Stat. Phys., 172:2, SI (2018), 611–626
P. Chleboun, A. Faggionato, F. Martinelli, C. Toninelli, “Mixing Length Scales of Low Temperature Spin Plaquettes Models”, J Stat Phys, 169:3 (2017), 441
Michael J. Kastoryano, Fernando G. S. L. Brandão, “Quantum Gibbs Samplers: The Commuting Case”, Commun. Math. Phys., 344:3 (2016), 915
S. Shlosman, “From the seminar on Mathematical Statistical Physics in Moscow State University, 1962–1994. Constructive criteria”, EPJ H, 37:4 (2012), 595
Vadim Shcherbakov, Anatoly Yambartsev, “On Equilibrium Distribution of a Reversible Growth Model”, J Stat Phys, 148:1 (2012), 53
Gibbs Measures and Phase Transitions, 2011, 495
A. G. Basuev, “Ising model in half-space: A series of phase transitions in low
magnetic fields”, Theoret. and Math. Phys., 153:2 (2007), 1539–1574
Emilio N. M. Cirillo, Enzo Olivieri, “Renormalization group at criticality and complete analyticity of constrained models: A numerical study”, J Stat Phys, 86:5-6 (1997), 1117
Karl Haller, Tom Kennedy, “Absence of renormalization group pathologies near the critical temperature. Two examples”, J Stat Phys, 85:5-6 (1996), 607
Etienne Laroche, “Hypercontractivité pour des systèmes de spins de portée infinie”, Probab. Th. Rel. Fields, 101:1 (1995), 89
Roberto H. Schonmann, Senya B. Shlosman, “Complete analyticity for 2D Ising completed”, Commun.Math. Phys., 170:2 (1995), 453
F. Martinelli, E. Olivieri, R. H. Schonmann, “For 2-D lattice spin systems weak mixing implies strong mixing”, Commun.Math. Phys., 165:1 (1994), 33
F. Martinelli, E. Olivieri, “Approach to equilibrium of Glauber dynamics in the one phase region”, Commun.Math. Phys., 161:3 (1994), 447
Aernout C. D. van Enter, Roberto Fernández, Alan D. Sokal, “Regularity properties and pathologies of position-space renormalization-group transformations: Scope and limitations of Gibbsian theory”, J Stat Phys, 72:5-6 (1993), 879
Pavel Kotalík, “Non-unicity of Gibbs states of Czech models in a half-space”, Czech J Phys, 41:10 (1991), 891
Christian Maes, Senya B. Shlosman, “Ergodicity of probabilistic cellular automata: A constructive criterion”, Commun.Math. Phys., 135:2 (1991), 233
Gibbs Measures and Phase Transitions, 1988
E. A. Pechersky, S. B. Shlosman, “Low-temperature phase transitions in systems with one ground state”, Theoret. and Math. Phys., 70:3 (1987), 325–330
S. B. Shlosman, “Unusual analytic properties of some lattice models: Complement of Lee–Yang theory”, Theoret. and Math. Phys., 69:2 (1986), 1147–1150
Citation in format AMSBIB
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