Thermodynamics of four-fermion models in the <span class="aps-inline-formula"><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>δ</mi></math></span> expansion

Sunil K. Gandhi; Marcus B. Pinto

doi:10.1103/PhysRevD.49.4258

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Thermodynamics of four-fermion models in the $δ$ expansion

Sunil K. Gandhi

Marcus B. Pinto

Department of Physics, University of Manchester, Manchester M13 9PL, United Kingdom

Departamento de Física, Universidade Federal de Santa Catarina, Florianópolis, S.C. 88.040-900, Brazil

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Phys. Rev. D 49, 4258 – Published 15 April, 1994

DOI: https://doi.org/10.1103/PhysRevD.49.4258

Abstract

Using the linear $δ$ expansion we investigate the free energy of the 1 + 1 and 2 + 1 dimensional Gross-Neveu model. In both cases the large- $N$ result is exactly reproduced at first order in $δ$ . However, when higher-order corrections are included our results for the phase transition differ both quantitatively and qualitatively from the large- $N$ predictions. In particular, our result for the critical temperature in 1 + 1 dimensions is in better with a general theorem for phase transitions in one space dimension.

References (21)

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S. K. Gandhi and M. B. Pinto, Phys. Rev. D 46, 2570 (1992)
D. Bailin and A. Love, Introduction to Gauge Field Theory (Adam Higler, Bristol, 1986) R. J. Rivers, Path Integral Methods in Quantum Field Theory (CUP, Cambridge, 1987) L. Dolan and R. Jackiw, Phys. Rev. D 9, 3320 (1974)
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[c1] A. Duncan and M. Moshe, Phys. Lett. B 215, 352 (1988)

[c2] A. Okopińska, Phys. Rev. D 35, 1835 (1987)

[c3] D. J. Gross and A. Neveu, Phys. Rev. D 10, 3235 (1974)

[c4] L. Jacobs, Phys. Rev. D 10, 3956 (1974) B. J. Harrington and A. Yildiz, ibid. 11, 779 (1974)

[c5] B. Rosenstein, B. J. Warr, and S. H. Park, Phys. Rev. D 39, 3088 (1988)

[c6] A. Okopińska, Phys. Rev. D 38, 2507 (1988)

[c7] R. F. Dashen, S.-K. Ma, and R. Rajaraman, Phys. Rev. D 11, 1499 (1975)

[c8] L. D. Landau and E. M. Lifshtiz, Statistical Physics (Pergamon, New York, 1958), p. 482

[c9] C. M. Bender et al., Phys. Rev. Lett. 58, 2615 (1987)

[c10] C. M. Bender and A. Rebhan, Phys. Rev. D 41, 3269 (1990)

[c11] P. M. Stevenson and I. Stancu, Phys. Rev. D 42, 2710 (1990)

[c12] S. K. Gandhi, H. F. Jones, and M. B. Pinto, Nucl. Phys. B359, 429 (1991)

[c13] S. K. Gandhi and M. B. Pinto, Phys. Rev. D 46, 2570 (1992)

[c14] D. Bailin and A. Love, Introduction to Gauge Field Theory (Adam Higler, Bristol, 1986) R. J. Rivers, Path Integral Methods in Quantum Field Theory (CUP, Cambridge, 1987) L. Dolan and R. Jackiw, Phys. Rev. D 9, 3320 (1974)

[c15] H. F. Jones and M. Monoyios, Int. J. Mod. Phys. A 4, 17 (1989)

[c16] C. M. Bender et al., Phys. Rev. D 37, 1472 (1988)

[c17] P. M. Stevenson, Phys. Rev. D 23, 2916 (1981)

[c18] C. M. Bender, Boettcher, and K. A. Milton, J. Math. Phys. 32, 3031 (1991)

[c19] I. Buckley, A. Duncan, and H. F. Jones, Phys. Rev. D 47, 2554 (1993) A. Duncan and H. F. Jones, ibid. 47, 2560 (1993)

[c20] T. Barnes and G. I. Gandhour, Phys. Rev. D 22, 924 (1980)

[c21] H. F. Jones and M. Moshe, Phys. Lett. B 234, 492 (1990)

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Thermodynamics of four-fermion models in the $δ$ expansion

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Thermodynamics of four-fermion models in the δ expansion

Abstract

References (21)

Thermodynamics of four-fermion models in the $δ$ expansion