Critical Behavior of a Supersymmetric Extension of the Ginzburg-Landau Model
Author(s)
Grigoris Panotopoulos
ABSTRACT
We make a connection between quantum phase transitions in condensed matter systems, and supersymmetric gauge theories that are of interest in the particle physics literature. In particular, we point out interesting effects of the supersymmetric quantum electrodynamics upon the critical behavior of the Ginzburg-Landau model. It is shown that supersymmetry fixes the critical exponents, as well as the Landau-Ginzburg para- meter, and that the model resides in the type II regime of superconductivity.
We make a connection between quantum phase transitions in condensed matter systems, and supersymmetric gauge theories that are of interest in the particle physics literature. In particular, we point out interesting effects of the supersymmetric quantum electrodynamics upon the critical behavior of the Ginzburg-Landau model. It is shown that supersymmetry fixes the critical exponents, as well as the Landau-Ginzburg para- meter, and that the model resides in the type II regime of superconductivity.
Cite this paper
nullG. Panotopoulos, "Critical Behavior of a Supersymmetric Extension of the Ginzburg-Landau Model," Journal of Modern Physics, Vol. 2 No. 5, 2011, pp. 374-378. doi: 10.4236/jmp.2011.25046.
nullG. Panotopoulos, "Critical Behavior of a Supersymmetric Extension of the Ginzburg-Landau Model," Journal of Modern Physics, Vol. 2 No. 5, 2011, pp. 374-378. doi: 10.4236/jmp.2011.25046.
References
[1] V. L. Ginzburg and L. D. Landau, “On the Theory of Superconductivity,” Zhurnal Eksperimental’noi i Teoreticheskoi Fiziki, Vol. 20, 1950, pp. 1064-1082. [2] B. I. Halperin, T. C. Lubensky and S. K. Ma, “First- Order Phase Transitions in Superconductors and Smectic-A Liquid Crystals,” Physical Review Letters, Vol. 32, 1974, pp. 292-295. J. H. Chen, T. C. Lubensky and D. R. Nelson, “Crossover near Fluctuation-Induced First-Order Phase Transitions in Superconductors,” Physical Review B, Vol. 17, No. 11, 1978, pp. 4274-4286. doi:10.1103/PhysRevB.17.4274 [3] I. D. Lawrie, “On the Phase Transitions in Abelian Higgs Models,” Nuclear Physics B, Vol. 200, No. 1, 1982, pp. 1-19. doi:10.1016/0550-3213(82)90055-4 I. F. Herbut and Z. Tesanovic, “Critical Fluctuations in Superconductors and the Magnetic Field Penetration Depth,” Physical Review Letters, Vol. 76, No. 24, 1996, pp. 4588-4591. doi:10.1103/PhysRevLett.76.4588 [4] H. Kleinert and F. S. Nogueira, “Critical Behavior of the Ginzburg-Landau Model Coupled to Massless Dirac Fermions,” Physical Review B, Vol. 66, No. 1, 2002, p. 012504. doi:10.1103/PhysRevB.66.012504 [5] J. B. Marston, “U(1) Gauge Theory of the Heisenberg Antiferromagnet,” Physical Review Letters, Vol. 61, No. 17, 1988, pp. 1914-1917. doi:10.1103/PhysRevLett.61.1914 J. B. Marston and I. Affleck, “Large-n Limit of the Hubbard-Heisenberg Model,” Physical Review B, Vol. 39, No. 16, 1989, pp. 11538-11558. doi:10.1103/PhysRevB.39.11538 D. H. Kim and P. A. Lee, “Theory of Spin Excitations in Undoped and Underdoped Cuprates,” Annals of Physics, Vol. 272, No. 1, 1999, pp. 130-164. doi:10.1006/aphy.1998.5888 [6] H. Kleinert, “Disorder Version of the Abelian Higgs Model and the Order of the Superconductive Phase Transition,” Lettere Al Nuovo Cimento, Vol. 35, No. 13, 1982, pp. 405-412. doi:10.1007/BF02754760 [7] S. Mo, J. Hove and A. Sudbo, “Order of the Metal-to-Superconductor Transition,” Physical Review B, Vol. 65, No. 10, 2002, p. 104501. doi:10.1103/PhysRevB.65.104501 [8] M. Le Bellac, “Quantum and Statistical Field Theory,” Oxford University Press, Oxford, 1992. [9] H. Kleinert and V. Schulte-Frohlinde, “Critical Phenomena in -Theory,” World Scientific, Singapore, 2001. http://www.physik.fu-berlin.de/kleinert/b8 [10] W. Hollik, E. Kraus and D. Stockinger, “Renormalization and Symmetry Conditions in Supersymmetric QED,” European Physical Journal C, Vol. 11, No. 2, 1999, pp. 365-381. doi:10.1007/s100529900216 [11] S. Ferrara and O. Piguet, “Perturbation Theory and Renormalization of Supersymmetric Yang-Mills Theories,” Nuclear Physics B, Vol. 93, No. 2, 1975, pp. 261-302. doi:10.1016/0550-3213(75)90573-8 [12] J. D. Bjorken and S. D. Drell, “Relativistic Quantum Mechanics,” McGraw-Hill, New York, 1998. [13] F. S. Nogueira and H. Kleinert, “Field Theoretical Approaches to the Superconducting Phase Transition,” The Smithsonian/NASA Astrophysics Data System. [14] M. E. Peskin and D. V. Schroeder, “An Introduction to Quantum Field Theory (Frontiers in Physics),” Westview Press, New York, 1995. M. Srednicki, “Quantum Field Theory,” Cambridge University Press, Cambridge, 2007. [15] G. ‘t Hooft and M. J. G. Veltman, “Regularization and Renormalization of Gauge Fields,” Nuclear Physics B, Vol. 44, No. 1, 1972, pp. 189-213. doi:10.1016/0550-3213(72)90279-9 [16] M. E. Machacek and M. T. Vaughn, “Two-Loop Renormalization Group Equations in a General Quantum Field Theory: (I). Wave Function Renormalization,” Nuclear Physics B, Vol. 222, No. 1, 1983, pp. 83-103. doi:10.1016/0550-3213(83)90610-7 [17] J. Wess and J. Bagger, “Supersymmetry and Supergravity,” Princeton University Press, New Jersey, 1992. [18] P. Fayet and J. Iliopoulos, “Spontaneously Broken Super- gauge Symmetries and Goldstone Spinors,” Physics Letters B, Vol. 51, No. 5, 1974, pp. 461-464. doi:10.1016/0370-2693(74)90310-4
[1] V. L. Ginzburg and L. D. Landau, “On the Theory of Superconductivity,” Zhurnal Eksperimental’noi i Teoreticheskoi Fiziki, Vol. 20, 1950, pp. 1064-1082. [2] B. I. Halperin, T. C. Lubensky and S. K. Ma, “First- Order Phase Transitions in Superconductors and Smectic-A Liquid Crystals,” Physical Review Letters, Vol. 32, 1974, pp. 292-295. J. H. Chen, T. C. Lubensky and D. R. Nelson, “Crossover near Fluctuation-Induced First-Order Phase Transitions in Superconductors,” Physical Review B, Vol. 17, No. 11, 1978, pp. 4274-4286. doi:10.1103/PhysRevB.17.4274 [3] I. D. Lawrie, “On the Phase Transitions in Abelian Higgs Models,” Nuclear Physics B, Vol. 200, No. 1, 1982, pp. 1-19. doi:10.1016/0550-3213(82)90055-4 I. F. Herbut and Z. Tesanovic, “Critical Fluctuations in Superconductors and the Magnetic Field Penetration Depth,” Physical Review Letters, Vol. 76, No. 24, 1996, pp. 4588-4591. doi:10.1103/PhysRevLett.76.4588 [4] H. Kleinert and F. S. Nogueira, “Critical Behavior of the Ginzburg-Landau Model Coupled to Massless Dirac Fermions,” Physical Review B, Vol. 66, No. 1, 2002, p. 012504. doi:10.1103/PhysRevB.66.012504 [5] J. B. Marston, “U(1) Gauge Theory of the Heisenberg Antiferromagnet,” Physical Review Letters, Vol. 61, No. 17, 1988, pp. 1914-1917. doi:10.1103/PhysRevLett.61.1914 J. B. Marston and I. Affleck, “Large-n Limit of the Hubbard-Heisenberg Model,” Physical Review B, Vol. 39, No. 16, 1989, pp. 11538-11558. doi:10.1103/PhysRevB.39.11538 D. H. Kim and P. A. Lee, “Theory of Spin Excitations in Undoped and Underdoped Cuprates,” Annals of Physics, Vol. 272, No. 1, 1999, pp. 130-164. doi:10.1006/aphy.1998.5888 [6] H. Kleinert, “Disorder Version of the Abelian Higgs Model and the Order of the Superconductive Phase Transition,” Lettere Al Nuovo Cimento, Vol. 35, No. 13, 1982, pp. 405-412. doi:10.1007/BF02754760 [7] S. Mo, J. Hove and A. Sudbo, “Order of the Metal-to-Superconductor Transition,” Physical Review B, Vol. 65, No. 10, 2002, p. 104501. doi:10.1103/PhysRevB.65.104501 [8] M. Le Bellac, “Quantum and Statistical Field Theory,” Oxford University Press, Oxford, 1992. [9] H. Kleinert and V. Schulte-Frohlinde, “Critical Phenomena in -Theory,” World Scientific, Singapore, 2001. http://www.physik.fu-berlin.de/kleinert/b8 [10] W. Hollik, E. Kraus and D. Stockinger, “Renormalization and Symmetry Conditions in Supersymmetric QED,” European Physical Journal C, Vol. 11, No. 2, 1999, pp. 365-381. doi:10.1007/s100529900216 [11] S. Ferrara and O. Piguet, “Perturbation Theory and Renormalization of Supersymmetric Yang-Mills Theories,” Nuclear Physics B, Vol. 93, No. 2, 1975, pp. 261-302. doi:10.1016/0550-3213(75)90573-8 [12] J. D. Bjorken and S. D. Drell, “Relativistic Quantum Mechanics,” McGraw-Hill, New York, 1998. [13] F. S. Nogueira and H. Kleinert, “Field Theoretical Approaches to the Superconducting Phase Transition,” The Smithsonian/NASA Astrophysics Data System. [14] M. E. Peskin and D. V. Schroeder, “An Introduction to Quantum Field Theory (Frontiers in Physics),” Westview Press, New York, 1995. M. Srednicki, “Quantum Field Theory,” Cambridge University Press, Cambridge, 2007. [15] G. ‘t Hooft and M. J. G. Veltman, “Regularization and Renormalization of Gauge Fields,” Nuclear Physics B, Vol. 44, No. 1, 1972, pp. 189-213. doi:10.1016/0550-3213(72)90279-9 [16] M. E. Machacek and M. T. Vaughn, “Two-Loop Renormalization Group Equations in a General Quantum Field Theory: (I). Wave Function Renormalization,” Nuclear Physics B, Vol. 222, No. 1, 1983, pp. 83-103. doi:10.1016/0550-3213(83)90610-7 [17] J. Wess and J. Bagger, “Supersymmetry and Supergravity,” Princeton University Press, New Jersey, 1992. [18] P. Fayet and J. Iliopoulos, “Spontaneously Broken Super- gauge Symmetries and Goldstone Spinors,” Physics Letters B, Vol. 51, No. 5, 1974, pp. 461-464. doi:10.1016/0370-2693(74)90310-4