Abstract:
Conditions of the existence of long range order and bounds on critical temperatures
are found for quantum models of rotators, quadrupoles and ferroelectrics. The method
used is based on combining infrared bounds with the technique of the Wiener integrals.
Citation:
L. A. Pastur, B. A. Khoruzhenko, “Phase transitions in quantum models of rotators and ferroelectrics”, TMF, 73:1 (1987), 111–124; Theoret. and Math. Phys., 73:1 (1987), 1094–1104
This publication is cited in the following 20 articles:
Piotr Stachura, Wiesław Pusz, Jacek Wojtkiewicz, “Non-existence of Bose–Einstein condensation in Bose–Hubbard model in dimensions 1 and 2”, Journal of Mathematical Physics, 61:11 (2020)
Jacek Wojtkiewicz, Wiesław Pusz, Piotr Stachura, “Bogolyubov inequality for the ground state and its application to interacting rotor systems”, Reports on Mathematical Physics, 80:2 (2017), 233
Jacek Wojtkiewicz, Wiesław Pusz, Piotr Stachura, “Operator Reflection Positivity Inequalities and their Applications to Interacting Quantum Rotors”, Reports on Mathematical Physics, 77:2 (2016), 183
Jacek Wojtkiewicz, “Long range order in the ground state of quantum interacting rotors in two dimensions”, Physica A: Statistical Mechanics and its Applications, 391:23 (2012), 5918
Yuri Kozitsky, Tatiana Pasurek, “Euclidean Gibbs Measures of Interacting Quantum Anharmonic Oscillators”, J Stat Phys, 127:5 (2007), 985
Alina Kargol, Yuri Kozitsky, “A Phase Transition in a Quantum Crystal with Asymmetric Potentials”, Lett Math Phys, 79:3 (2007), 279
Alexei L Rebenko, Valentin A Zagrebnov, “Gibbs state uniqueness for an anharmonic quantum crystal with a non-polynomial double-well potential”, J. Stat. Mech., 2006:09 (2006), P09002
Y. Kondratiev, Y. Kozitsky, Encyclopedia of Mathematical Physics, 2006, 376
Y Kondratiev, Y Kozitsky, Encyclopedia of Mathematical Physics, 2006, 197
Yuri Kozitsky, “Gap Estimates for Double-Well Schr�dinger Operators and Quantum Stabilization of Anharmonic Crystals”, Journal of Dynamics and Differential Equations, 16:2 (2004), 385
Sergio Albeverio, Yuri Kondratiev, Yuri Kozitsky, Michael Röckner, “Small Mass Implies Uniqueness of Gibbs States of a Quantum Crystal”, Commun. Math. Phys., 241:1 (2003), 69
S. ALBEVERIO, YU. KONDRATIEV, YU. KOZITSKY, M. RÖCKNER, “EUCLIDEAN GIBBS STATES OF QUANTUM LATTICE SYSTEMS”, Rev. Math. Phys., 14:12 (2002), 1335
S Albeverio, Yu.G Kondratiev, R.A Minlos, G.V Shchepan'uk, “Ground state euclidean measures for quantum lattice systems on compact manifolds”, Reports on Mathematical Physics, 45:3 (2000), 419
R. A. MINLOS, A. VERBEURE, V. A. ZAGREBNOV, “A QUANTUM CRYSTAL MODEL IN THE LIGHT-MASS LIMIT: GIBBS STATES”, Rev. Math. Phys., 12:07 (2000), 981
Corgini, M, “Gaussian domination in a quantum system of nonlinear oscillators”, Modern Physics Letters B, 13:12–13 (1999), 411
B. Helffer, Microlocal Analysis and Spectral Theory, 1997, 307
A Verbeure, V A Zagrebnov, “No-go theorem for quantum structural phase transitions”, J. Phys. A: Math. Gen., 28:18 (1995), 5415
Roman Gielerak, Robert Olkiewicz, “Gentle perturbations of the free Bose gas. I”, J Stat Phys, 80:3-4 (1995), 875
V. S. Barbulyak, Yu. G. Kondrat'ev, “The quasiclassical limit for the Schrödinger operator and phase transitions in quantum statistical physics”, Funct. Anal. Appl., 26:2 (1992), 124–126
V. S. Barbulyak, “Chessboard estimates and critical temperature in quantum lattice systems”, Ukr Math J, 43:11 (1991), 1466