Publication: Schwinger and Thirring models at finite chemical potential and temperature
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1998-03-15
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Amer Physical Soc
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Abstract
The imaginary time generating functional Z for the assless Schwinger model at nonzero chemical potential mu and temperature T is studied in a torus with spatial length L. The lack of Hermiticity of the Dirac operator gives rise to a nontrivial μ- and T-dependent phase J in the effective action. When the Dirac operator has no zero modes (trivial sector), we evaluate J, which is a topological contribution, and we find exactly Z, the thermodynamical partition function, the boson propagator and the thermally averaged Polyakov loop. The μ-dependent contribution of the free partition function cancels exactly the nonperturbative one from J, for L→∞, yielding a zero charge density for the system, which bosonizes at nonzero μ. The boson mass is e/√π, independent of T and μ, which is also the inverse correlation length between two opposite charges. Both the boson propagator and the Polyakov loop acquire a new T- and μ -dependent term at L→∞,. The imaginary time generating functional for the massless Thirring model at nonzero T and μ is obtained exactly in terms of the above solution of the Schwinger model in the trivial sector. For this model, the μ dependences of the thermodynamical partition function, the total fermion number density and the fermion two- point correlation function are obtained. The phase J displayed here leads to our new results and allows us to complement nontrivially previous studies on those models.
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© 1998 The American Physical Society.
This work was supported in part by the European Commission under the Human Capital and Mobility program contract number ERB-CHRX-CT94-0423. The financial support of CICYT, projects AEN96-1634 and AEN97-1693, is also acknowledged. One of us (A.G.N.) has received financial support from Spanish Ministry of Education and Culture, 57 SCHWINGER AND THIRRING MODELS AT FINITE... 3631 through the ‘‘Perfeccionamiento de Doctores y Tecnólogos en el Extranjero’’ program and he is very grateful to Professor T. W. B. Kibble, Professor R. Rivers, and Professor T. Evans of the Theory Group at Imperial College, for their kind hospitality and for useful discussions and suggestions. We are also grateful to Professor F. Ruiz Ruiz for providing some useful information.
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