Lattice QCD at finite isospin density at zero and finite temperature

J. B. Kogut; D. K. Sinclair

doi:10.1103/PhysRevD.66.034505

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Lattice QCD at finite isospin density at zero and finite temperature

J. B. Kogut

D. K. Sinclair

Department of Physics, University of Illinois, 1110 West Green Street, Urbana, Illinois 61801-3080

HEP Division, Argonne National Laboratory, 9700 South Cass Avenue, Argonne, Illinois 60439

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Phys. Rev. D 66, 034505 – Published 22 August, 2002

DOI: https://doi.org/10.1103/PhysRevD.66.034505

Abstract

We simulate lattice QCD with dynamical u and d quarks at finite chemical potential, $μ_{I},$ for the third component of isospin ${(I}_{3})$ at both zero and at finite temperature. At zero temperature there is some $μ_{I},$ $μ_{c}$ say, above which $I_{3}$ and parity are spontaneously broken by a charged pion condensate. This is in qualitative agreement with the prediction of effective (chiral) Lagrangians which also predict $μ_{c} {= m}_{π} .$ This transition appears to be second order, with scaling properties consistent with the mean-field predictions of such effective Lagrangian models. We have also studied the restoration of $I_{3}$ symmetry at high temperature for $μ_{I} > μ_{c} .$ For $μ_{I}$ sufficiently large, this finite temperature phase transition is very abrupt, suggesting that it is first order. As $μ_{I}$ is decreased it appears to become second order connecting continuously with the zero temperature transition.

References (16)

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J.B. Kogut and D.K. Sinclair, Nucl. Phys. B (Proc. Suppl.) 106, 444 (2002).
D.T. Son and M.A. Stephanov, Phys. Rev. Lett. 86, 592 (2001); Yad. Fiz. 64, 899 (2001) [Phys. At. Nucl. 64, 834 (2001)].
J.B. Kogut and D.K. Sinclair, Phys. Rev. D 66, 014508 (2002); S. Gupta, hep-lat/0202005.
S. Hands, J.B. Kogut, M.-P. Lombardo, and S.E. Morrison, Nucl. Phys. B558, 327 (1999); J.B. Kogut, D.K. Sinclair, S.J. Hands, and S.E. Morrison, Phys. Rev. D 64, 094505 (2001).
R. Aloisio, V. Azcoiti, G. Di Carlo, A. Galante, and A.F. Grillo, Phys. Lett. B 493, 189 (2000); Nucl. Phys. B606, 322 (2001).
A. Nakamura, Phys. Lett. 149B, 391 (1984); S. Muroya, A. Nakamura, and C. Nonaka, nucl-th/0111082.
J.B. Kogut, D. Toublan, and D.K. Sinclair, hep-lat/0205019.
J.B. Kogut, M.A. Stephanov, and D. Toublan, Phys. Lett. B 464, 183 (1999); J.B. Kogut, M.A. Stephanov, D. Toublan, J.J.M. Verbaarschot, and A. Zhitnitsky, Nucl. Phys. B582, 477 (2000).
J.B. Kogut, D. Toublan, and D.K. Sinclair, Phys. Lett. B 514, 77 (2001).
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J.B. Kogut and D. Toublan, Phys. Rev. D 64, 034007 (2001).

[c1] Z. Fodor and S.D. Katz, Phys. Lett. B 534, 87 (2002); J. High Energy Phys. 03, 014 (2002); S. Choe et al., Phys. Rev. D 65, 054501 (2002); C.R. Allton et al., hep-lat/0204010; P. de Forcrand and O. Philipsen, hep-lat/0205016; P.R. Crompton, Nucl. Phys. B619, 499 (2001); ibid.B626, 228 (2002).

[c2] J.B. Kogut and D.K. Sinclair, Nucl. Phys. B (Proc. Suppl.) 106, 444 (2002).

[c3] D.T. Son and M.A. Stephanov, Phys. Rev. Lett. 86, 592 (2001); Yad. Fiz. 64, 899 (2001) [Phys. At. Nucl. 64, 834 (2001)].

[c4] J.B. Kogut and D.K. Sinclair, Phys. Rev. D 66, 014508 (2002); S. Gupta, hep-lat/0202005.

[c5] S. Hands, J.B. Kogut, M.-P. Lombardo, and S.E. Morrison, Nucl. Phys. B558, 327 (1999); J.B. Kogut, D.K. Sinclair, S.J. Hands, and S.E. Morrison, Phys. Rev. D 64, 094505 (2001).

[c6] R. Aloisio, V. Azcoiti, G. Di Carlo, A. Galante, and A.F. Grillo, Phys. Lett. B 493, 189 (2000); Nucl. Phys. B606, 322 (2001).

[c7] A. Nakamura, Phys. Lett. 149B, 391 (1984); S. Muroya, A. Nakamura, and C. Nonaka, nucl-th/0111082.

[c8] J.B. Kogut, D. Toublan, and D.K. Sinclair, hep-lat/0205019.

[c9] J.B. Kogut, M.A. Stephanov, and D. Toublan, Phys. Lett. B 464, 183 (1999); J.B. Kogut, M.A. Stephanov, D. Toublan, J.J.M. Verbaarschot, and A. Zhitnitsky, Nucl. Phys. B582, 477 (2000).

[c10] J.B. Kogut, D. Toublan, and D.K. Sinclair, Phys. Lett. B 514, 77 (2001).

[c11] I.D. Lawrie and S. Sarbach, in Phase Transitions and Critical Phenomena (Academic Press, London, 1972), Vol. 9.

[c12] K. Splittorff, D. Toublan, and J.J.M. Verbaarschot, Nucl. Phys. B620, 290 (2002).

[c13] F.R. Brown et al., Phys. Rev. Lett. 61, 2058 (1988).

[c14] P. Bacilieri et al., Phys. Rev. Lett. 61, 1545 (1988).

[c15] D.T. Son, M.A. Stephanov, and A.R. Zhitnitsky, Phys. Lett. B 510, 167 (2001).

[c16] J.B. Kogut and D. Toublan, Phys. Rev. D 64, 034007 (2001).

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Lattice QCD at finite isospin density at zero and finite temperature

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References (16)

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