JMP  Vol.4 No.2 , February 2013
Critical Exponents of Quark Matter
Abstract: I investigate the ferromagnetic phase transition inside strong quark matter (SQM) with one gluon exchange interaction between strong quarks. I use a variational method and the Landau-Fermi liquid theory and obtain the thermodynamics quantities of SQM. In the low temperature limit, the equation of state (EOS) and critical exponents for the second-order phase transition (ferromagnetic phase transition) in SQM are analytically calculated. The results are in agreement with the Ginzberg-Landau theory.
Cite this paper: H. Gholizade, "Critical Exponents of Quark Matter," Journal of Modern Physics, Vol. 4 No. 2, 2013, pp. 280-284. doi: 10.4236/jmp.2013.42038.

[1]   T. Tatsumi and K. Sato, “Non-Fermi-Liquid Effect in Magnetic Susceptibility,” Physics Letters B, Vol. 672, No. 2, 2009, pp. 132-135. doi:10.1016/j.physletb.2008.12.064

[2]   M. Bigdeli, G. H. Bordbar and Z. Rezaei, “Temperature Dependence of Magnetic Susceptibility of Nuclear Matter: Lowest Order Constrained Variational Calculations,” Physical Review C, Vol. 80, No. 3, 2009, 8 p. doi:10.1103/PhysRevC.80.034310

[3]   Y. Zhang and D. Sarama, “Exchange Instabilities in Electron Systems: Bloch versus Stoner Ferromagnetism,” Physical Review B, Vol. 72, No. 11, 2005, 9 p. doi:10.1103/PhysRevB.72.115317

[4]   S. Ciccariello and A. De Col, “Zero-Temperature Perturbative Calculation of the Magnetic Susceptibility of the Free Fermion System,” European Journal of Physics, Vol. 22, No. 6, 2001, pp. 629-637. doi:10.1088/0143-0807/22/6/308

[5]   A. Uldry and R. J. Elliott, “The Two-Particle Propagator and Magnetic Susceptibility in the Hubbard Model,” Journal of Physics, Vol. 17, No. 19, 2005, p. 2903.

[6]   M. Ulmke, “Ferromagnetism in the Hubbard Model on Fcc-Type Lattices,” European Physics Journal B1, Vol. 1, No. 3, 1998, pp. 301-304. doi:10.1007/s100510050186

[7]   D. Bodea, M. Crisan, I. Grosu and I. Tifrea, “Large n-Expansion Limit of the Three-Dimensional Ferromagnetic Quantum Phase Transition,” Journal of Low Temperature Physics, Vol. 146, No. 3-4, 2007, pp. 315-327. doi:10.1007/s10909-006-9251-3

[8]   E. M. Chudnovsky, “Magnetic Susceptibility of Relativistic Fermi Gas,” Journal Physics A, Vol. 14, No. 8, 1981, pp. 2091. doi:10.1088/0305-4470/14/8/030

[9]   V. T. Rajan, “Magnetic Susceptibility and Specific Heat of the Coqblin-Schrieffer Model,” Physical Review Letters, Vol. 51, No. 4, 1983, pp. 308-311. doi:10.1103/PhysRevLett.51.308

[10]   L. Homorodean, “Magnetic Susceptibility of the Relativistic Boson Gas,” Modern Physics Letters B, Vol. 15, No. 25, 2001, p. 1147. doi:10.1142/S021798490100283X

[11]   T. M. A. Khajil, “Magnetic Susceptibility of Liquid Metals,” International Journal of Modern Physics B, Vol. 16, No. 1, 2002, p. 2221. doi:10.1142/S0217979202011160

[12]   N. Holden, B. T. Matthias, P. W. Anderson and H. W. Lewis, “New Low-Temperature Ferromagnets,” Physical Review, Vol. 102, No. 6, 1956, p. 1463. doi:10.1103/PhysRev.102.1463

[13]   T. Izuyama, “General Theorems on Ferromagnetism and Ferromagnetic Spin Waves,” Physical Review B, Vol. 5, No. 1, 1972, pp. 190-203. doi:10.1103/PhysRevB.5.190

[14]   K. Rajagopal and S. D. Mahanti, “Ferromagnetism of an Electron Gas,” Physical Review, Vol. 158, No. 2, 1967, pp. 353-355. doi:10.1103/PhysRev.158.353

[15]   G. Fabricius and A. M. Llois, “Ferromagnetic Stability and Density of States,” Physical Review B, Vol. 48, No. 9, 1993, pp. 6665-6667. doi:10.1103/PhysRevB.48.6665

[16]   P. C. Hemmer and D. Imbro, “Ferromagnetic Fluids,” Physical Review A, Vol. 16, No. 1, 1977, pp. 380-386. doi:10.1103/PhysRevA.16.380

[17]   Baladie and A. Buzdin, “Thermodynamic Properties of Ferromagnet/Superconductor/Ferromagnet Nanostructures,” Physical Review B, Vol. 67, No. 1, 2003, 9 p. doi:10.1103/PhysRevB.67.014523

[18]   Y. Kwon, D. M. Ceperly and R. M. Martin, “Quantum Monte Carlo Calculation of the Fermi-Liquid Parameters in the Two-Dimensional Electron Gas,” Physical Review B, Vol. 50, No. 3, 1994, p. 1684-1694. doi:10.1103/PhysRevB.50.1684

[19]   C. Attaccalite, S. Moroni, P. G. Giorgi and G. B. Bachelet, “Correlation Energy and Spin Polarization in the 2D Electron Gas,” Physical Review Letters, Vol. 88, No. 25, 2002, Article ID: 256601.

[20]   C. Attaccalite, S. Moroni, P. G. Giorgi and G. B. Bachelet, “Two-Dimensional Electron Gas: Correlation Energy versus Density and Spin Polarization,” International Journal of Quantum Chemistry, Vol. 91, No. 2, 2003, pp. 126-130.

[21]   K. Huang, “Statistical Mechanics,” 2nd Edition, John Wiley & Sons Ltd., Hoboken, 1987.

[22]   Landau and E. Lifshitz, “Statistical Physics Part II,” 3rd Edition, Pergamon Press, Oxford, 1988.

[23]   T. Tatsumi, “Ferromagnetism of Quark Liquid,” Physical Letters B, Vol. 489, No. 3-4, 2000, pp. 280-286. doi:10.1016/S0370-2693(00)00927-8

[24]   G. Baym and S. A. Chin, “Landau Theory of Relativistic Fermi Liquids,” Nuclear Physics A, Vol. 262, No. 3, 1976, pp. 527-538. doi:10.1016/0375-9474(76)90513-3

[25]   M. Modarres and H. Gholizade, “The Ferromagnetic Phase of Quark Matter in the Framework of One Gluon Exchange and Thermodynamics with the Density— Temperature-Dependent Particle Mass Mode,” Physica A: Statistical Mechanics and Its Applications, Vol. 387, No. 12, 2008, pp. 2761-2776. doi:10.1016/j.physa.2008.01.104

[26]   J. Sakurai, “Advanced Quantum Mechanics,” Pearson, London, 1967.

[27]   H. Kanzawa, K. Oyamatsu, K. Sumiyoshi and M. Takano, “Variational Calculation for the Equation of State of Nuclear Matter at Finite Temperatures,” Nuclear Physics A, Vol. 791, No. 1-2, 2007, pp. 232-250. doi:10.1016/j.nuclphysa.2007.01.098

[28]   J. W. Clark, “Variational Theory of Nuclear Matter,” Progress in Particle and Nuclear Physics, Vol. 2, 1979, pp. 89-199. doi:10.1016/0146-6410(79)90004-8

[29]   A. Akmal, V. R. Pandharipande and D. G. Ravenhall, “Equation of State of Nucleon Matter and Neutron Star Structure,” Physical Review C, Vol. 58, No. 3, 1998, pp. 1804-1828. doi:10.1103/PhysRevC.58.1804

[30]   R. B. Wiringa, V. G. J. Stokes and R. Schiavilla, “Accurate Nucleon-Nucleon Potential with Charge-Independence Breaking,” Physical Review C, Vol. 51, No. 3, 1995, pp. 38-51. doi:10.1103/PhysRevC.51.38

[31]   B. S. Pudliner, V. R. Pandharipande, J. Carlson and R. B. Wiringa, “Quantum Monte Carlo Calculations of A ≤6 Nuclei,” Physical Review Letters, Vol. 74, No. 22, 1995, pp. 4396-4399. doi:10.1103/PhysRevLett.74.4396

[32]   V. R. Pandharipande and R. B. Wiringa, “Variations on a Theme of Nuclear Matter,” Review Modern Physics, Vol. 51, No. 4, 1979, pp. 821-861. doi:10.1103/RevModPhys.51.821

[33]   B. Friedman and V. R. Pandharipande, “Hot and Cold, Nuclear and Neutron Matter,” Nuclear Physics A, Vol. 361, No. 2, 1981, pp. 502-520. doi:10.1016/0375-9474(81)90649-7

[34]   K. E. Schmidt and V. R. Pandharipande, “Variational Theory of Nuclear Matter at Finite Temperatures,” Physics Letters B, Vol. 87, No. 1-2, 1979, pp. 11-14. doi:10.1016/0370-2693(79)90004-2

[35]   M. Modarres, “LOCV Calculations of Pressure in Nuclear Matter at Finite Temperature,” Journal of Physics G: Nuclear and Particle Physics, Vol. 19, No. 9, 1993, pp. 1349-1358. doi:10.1088/0954-3899/19/9/013

[36]   H. Gholizade and D. Momeni, “Stability of Landau Fermi Liquid Theory,” Journal of Statistical Physics, Vol. 141, No. 6, 2010, pp. 957-969. doi:10.1007/s10955-010-0091-9